Computer Science Theory at Northeastern
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Theory Seminar
This semester the theory seminar will be held on Wednesdays 12:30  2 PM, and is being coorganized by Konstantina Bairaktari and Sushant Agarwal. Write to Konstantina with suggestions for speakers!Spring Semester, 2023
April 26 12:30 PM ISEC 655 
Anamay Chaturvedi Abstract In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the private data of individuals. However, when the size of the data stream drawn from the domain of the objective function is large or arrives very fast, one must privately optimize the objective within the constraints of the streaming setting. We establish fundamental differentially private baselines for this problem and then derive better tradeoffs between privacy and utility for the special case of decomposable submodular functions. A submodular function is decomposable when it can be written as a sum of submodular functions; this structure arises naturally when each summand function models the utility of an individual and the goal is to study the total utility of the whole population as in the wellknown Combinatorial Public Projects Problem. Finally, we complement our theoretical analysis with experimental corroboration. Joint work with Huy Nguyen and Thy Nguyen. 
April 12 12:30 PM ISEC 655 
Soheil Behnezhad Abstract Lineartime algorithms have long been the gold standard of algorithm design. But can we design algorithms that run even faster, i.e., in time *sublinear* in the input size? In this talk, I will show how this is possible for the fundamental maximum matching problem. I will also discuss how sublinear time algorithms for maximum matching can be used to answer a longstanding open problem in the area of dynamic algorithms for maintaining a better than 1/2 approximation of maximum matching in polylog time. 
March 1 12:30 PM ISEC 655 
Ethan Mook Abstract Can we design a private variant of "Google search" that would enable users to search the Internet privately without revealing their queries to Google? Fully homomorphic encryption gives a solution to this problem, where users would send their search queries to Google encrypted in a way that allows Google to compute the encrypted search results, without learning anything about the query itself. However, this solution would require Google to run a huge computation that touches the entire content of the Internet to answer each encrypted search query, making it realistically infeasible! Is there a way for Google to preprocess the Internet content into a special data structure that would allow it to answer any encrypted query efficiently by only accessing some small number of locations in the data structure? We give a solution to this problem as a special case of our work. Concretely, we construct the first schemes for "doubly efficient private information retrieval" and "fully homomorphic encryption in the RAM model" under standard cryptographic hardness assumptions (Ring Learning with Errors). Previously we only had heuristic candidate constructions that only satisfied relaxed variants of these primitives. Our new solutions combine tools from cryptography together with data structures for fast polynomial evaluation (Kedlaya and Umans '08). Based on: https://eprint.iacr.org/2022/1703. 
February 15 12:30 PM Ryder Hall 153 
Rajesh Jayaram Abstract We consider the problem of computing the cost of the Euclidean Minimum Spanning Tree (MST) of an npoint set X in R^d, where the points in X are presented in an arbitrary order stream of insertions and deletions. In the streaming setting, the goal is to maintain an approximation to the MST cost in small space. In low dimensions, (1+ε) approximations are possible in sublinear (in n) space [Frahling, Indyk, Sohler, SoCG '05]. However, for high dimensional spaces the best known approximation was Õ(log n), due to [Chen, Jayaram, Levi, Waingarten, STOC '22], and prior to that it was O(log^2 n) due to [Indyk, STOC '04] and [Andoni, Indyk, Krauthgamer, SODA '08]. In this talk, we describe the first algorithm which achieves a constant factor approximation to the Euclidean MST in sublinear space. Specifically, for any ε > 0, our algorithm obtains a Õ(1/ε^2) approximation in n^{O(ε)} space. We show the approximation is tight up to a constant, by proving an Omega(sqrt{n}) space lower bound for any algorithm that beats a 1.1 approximation. Furthermore, the algorithm can be modified to give a (1+ε) approximation in O(1/ε)passes over the stream, which separates the complexity for single vs multipass streaming. Joint work with Xi Chen, Vincent CohenAddad, Amit Levi, and Erik Waingarten (to appear in STOC '23). 
February 1 12:30 PM ISEC 655 
Jason Li Abstract Minimum cut problems are among the most wellstudied questions in combinatorial optimization. In this talk, I will introduce a simple but powerful new tool for solving minimum cut problems called the minimum isolating cuts. I will show how this tool can be employed to obtain faster algorithms for several fundamental mincut problems, namely global mincut, Steiner mincut, and allpairs mincut. For these problems, the new results represent the first improvement in their runtimes in several decades. These results are in collaboration with Amir Abboud, Robert Krauthgamer, Danupon Nanongkai, Thatchaphol Saranurak, and Ohad Trabelsi. 
January 25 12:30 PM Ryder Hall 153 
Zihan Tan Abstract Graph Crossing Number is a fundamental and extensively studied problem with wide ranging applications. In this problem, the goal is to draw an input graph G in the plane so as to minimize the number of crossings between the images of its edges. The problem is notoriously difficult, and despite extensive work, nontrivial approximation algorithms are only known for boundeddegree graphs. Even for this special case, the best current algorithm achieves a O(sqrt(n))approximation, while the best current negative results do not rule out constant factor approximation. All current approximation algorithms for the problem build on the same paradigm, which is also used in practice: compute a set E’of edges (called a planarizing set) such that G \ E’ is planar; compute a planar drawing of G \ E’; then add the drawings of the edges of E to the resulting drawing. Unfortunately, there are examples of graphs G, in which any implementation of this method must incur Ω(OPT^2) crossings, where OPT is the value of the optimal solution. This barrier seems to doom the only currently known approach to designing approximation algorithms for the problem, and to prevent it from yielding a better than O(sqrt(n))approximation. We propose a new paradigm that allows us to overcome this barrier. Using the new paradigm, we reduce the Crossing Number problem to Crossing Number with Rotation System – a variant of the Crossing Number problem, in which the ordering of the edges incident to every vertex is fixed as part of input. We then show a randomized algorithm for this new problem, that allows us to obtain a subpolynomial approximation for Graph Crossing Number on lowdegree graphs. This talk is based on joint work with Julia Chuzhoy and Sepideh Mahabadi. 
January 18 12:30 PM WVH 366 
Christopher Tosh Abstract Multigroup agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. This criterion addresses recent practical concerns in machine learning such as subgroup fairness and hidden stratification. In this talk, we will discuss the structure of solutions to the multigroup learning problem and provide corresponding simple and nearoptimal algorithms. 
Fall Semester, 2022
December 7 12:30 PM ISEC 655 
François Sellier Abstract We consider the maximum weight bmatching problem, assuming all weights are small integers drawn from [1,W]. We design a generalized weighted version of edgedegree constrained subgraphs (EDCS), a matching sparsifier originally developed by Bernstein and Stein that have been used for dynamic and streaming matchings in graphs. Our new subgraph has bounded vertex degrees (hence uses only a small number of edges) and can be easily computed. Moreover, it contains a (2  1/(2W) + epsilon) approximation of the maximum weight matching. 
November 30 12:30 PM ISEC 655 
Eysa Lee Abstract We propose a secure multiparty signing protocol for the BBS+ signature scheme; in other words, an anonymous credential scheme with threshold issuance. We prove that due to the structure of the BBS+ signature, simply verifying the signature produced by an otherwise semihonest protocol is sufficient to achieve composable security against a malicious adversary. Consequently, our protocol is extremely simple and efficient: it involves a single request from the client (who requires a signature) to the signing parties, one roundtrip communication among the signing parties, and finally a response to the client; in some deployment scenarios the concrete cost bottleneck may be the client's local verification of the signature that it receives. Furthermore, our protocol can be extended to support stronglyblind signing and to serve as a distributed evaluation protocol for the DodisYampolskiy Oblivious VRF. We validate our efficiency claims by implementing and benchmarking our protocol. This is joint work with Jack Doerner, Yashvanth Kondi, abhi shelat, and LaKyah Tyner. 
November 16 12:30 PM WVH 366 
Daniel Reichman Abstract Networks can be conductive to the spread of undesirable phenomena from false information to bankruptcy of financial institutions and contagious disease. How can we leverage algorithms to stop or slow down contagious processes? I will survey some of the literature focusing mostly on the bootstrap percolation model which is a simple contagion model where every uninfected node is infected if it has at least r infected neighbors for some r>1. I will present some improved algorithms for the binomial random graph and conclude with several open questions. Based on joint works with Hermish Mehta, Uri Feige, Michael Krivelevich and Amin CojaOghlan. 
November 9 12:30 PM ISEC 655 
AnthimosVardis Kandiros Abstract Statistical estimation has largely focused on estimating models from independent and identically distributed observations. This assumption is, however, too strong. In many applications, observations are collected on nodes of a network, or some spatial or temporal domain, and are dependent. Examples abound in financial and meteorological applications, and dependencies naturally arise in social networks through peer effects. We study statistical estimation problems wherein responses at the nodes of a network are not independent conditioning on the nodes’ features but dependent. We model their dependencies through a Markov Random Field with a logdensity that captures individual effects and peer effects. Importantly, we allow dependencies to be substantial, i.e do not assume that the Markov Random Field is in high temperature. Our model generalizes the standard statistical estimation model with independent observations which is obtained by setting the temperature to infinity. As our main contribution we provide algorithms and statistically efficient estimation rates for our model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network estimation problems with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a single sample. Based on joint works with Yuval Dagan, Constantinos Daskalakis, Nishanth Dikkala and Surbhi Goel. 
November 2 12:30 PM ISEC 655 
Bogdan Kulynych Abstract
Having similar behavior at training time and test time — what we call
a “What You See Is What You Get” (WYSIWYG) property — is
desirable in machine learning. Models trained with standard
stochastic gradient descent (SGD), however, do not necessarily have
this property, as their complex behaviors such as robustness or
subgroup performance can differ drastically between training and test
time. In contrast, we show that DifferentiallyPrivate (DP) training
provably ensures the highlevel WYSIWYG property, which we quantify
using a notion of Distributional Generalization (DG). Applying this
connection, we introduce new conceptual tools for designing
deeplearning methods by reducing generalization concerns to
optimization ones: to mitigate unwanted behavior at test time, it is
provably sufficient to mitigate this behavior on the training data.
By applying this novel design principle, which bypasses
“pathologies” of SGD, we
construct simple algorithms that are competitive with SOTA in several
distributionalrobustness applications, significantly improve the
privacy vs. disparate impact tradeoff of DPSGD, and mitigate robust
overfitting in adversarial training. Finally, we also improve on
theoretical bounds relating DP, stability, and distributional
generalization. This talk is based on the upcoming NeurIPS 2022
“What
You See is What You Get: Principled Deep Learning via Distributional
Generalization” paper by Bogdan Kulynych (EPFL), YaoYuan Yang (UC
San Diego), Yaodong Yu (UC Berkeley), Jarosław Błasiok
(Columbia University), and Preetum Nakkiran (UC San Diego). The
preprint version is available at
https://arxiv.org/abs/2204.03230.

October 26 1:00 PM Hybrid, Richards Hall 238 
Pratik Chaudhari Abstract Accepted statistical wisdom suggests that larger the model class, the more likely it is to overfit the training data. And yet, deep networks generalize extremely well. The larger the deep network, the better its accuracy on new data. This talk seeks to shed light upon this apparent paradox. We will argue that deep networks are successful because of a characteristic structure in the space of learning tasks. The input correlation matrix for typical tasks has a peculiar (“sloppy”) eigenspectrum where, in addition to a few large eigenvalues (salient features), there are a large number of small eigenvalues that are distributed uniformly over a very large range. This structure in the input data is strongly mirrored in the representation learned by the network. A number of quantities such as the Hessian, the Fisher Information Matrix, as well as others such as correlations of activations or Jacobians, are also sloppy. Even if the model class for deep networks is very large, there is only a tiny subset of models that fit such sloppy tasks. Using these ideas, this talk will demonstrate an analytical nonvacuous generalization bound for deep networks that does not use compression. It will also discuss how these ideas can be harnessed into algorithms that learn from unlabeled data optimally. References 
October 19 1:00 PM Hybrid, West Village H 366 
Santhoshini Velusamy Abstract Constraint satisfaction problems (CSPs) are ubiquitous in computer science and encompass optimization problems such as MaxCUT, MaxDICUT, MaxkSAT, MaxqColoring, Unique Games, etc. Until recently, MaxCUT and a couple of other Max2CSPs were the only CSPs studied in the streaming setting. In this talk, I will first describe our results giving new upper and lower bounds on the approximability of every CSP in the singlepass streaming setting. In particular, we prove the following theorem: For every CSP, there is a constant α such that the CSP is αapproximable in polylogarithmic space by a linear sketching algorithm and any sketching algorithm that beats αapproximation requires polynomial space. I will conclude with some interesting results from recent followup works and also discuss open problems in this direction. 
September 28 12:30 PM Richards Hall 238 
Nicole Wein Abstract A shortcut set is a (small) set of edges that when added to a directed graph G produces a graph with the same reachability structure as G while reducing the diameter as much as possible. A hopset is defined similarly but for approximate distances instead of reachability. One motivation for such structures is that in many settings (e.g. distributed, parallel, dynamic, streaming), computation is faster when the diameter of the graph is small. Thus, to compute, for instance, streachability in such a setting, it is useful to find a shortcut set as a preprocessing step, and then run an streachability algorithm on the resulting graph. This talk is about existential bounds for shortcut sets and hopsets: given a budget of ~O(n) added edges, what is the smallest diameter achievable? A folklore algorithm says that diameter O(n^{1/2}) is possible for any graph. A recent breakthrough of Kogan and Parter improves this to O(n^{1/3}) for shortcut sets and O(n^{2/5}) for hopsets. In recent work, we ask whether hopsets (approximate distances) are truly harder than shortcut sets (reachability). We close the gap between hopsets and shortcut sets by providing an O(n^{1/3})diameter construction for hopsets. Joint work with Aaron Bernstein. 
Spring Semester, 2022
April 28 11AM ISEC 655 (inperson)/Zoom 
Lucianna Kiffer Abstract In cryptocurrencies, the block reward is meant to serve as the incentive mechanism for miners to commit resources to create blocks and in effect secure the system. Existing systems primarily divide the reward in proportion to expended resources and follow one of two static models for total block reward: (i) a fixed reward for each block (e.g., Ethereum), or (ii) one where the block reward halves every set number of blocks (e.g., the Bitcoin model of halving roughly every 4 years) but otherwise remains fixed between halvings. In recent work, a gametheoretic analysis of the static model under asymmetric miner costs showed that an equilibrium always exists and is unique [1]. Their analysis also reveals how asymmetric costs can lead to largescale centralization in blockchain mining, a phenomenon that has been observed in Bitcoin and Ethereum and highlighted by other studies including [2,3]. In this work we introduce a novel family of mining reward functions, HaPPYMine (HAshPegged Proportional Yield), which peg the value of the reward to the hashrate of the system, decreasing the reward as the hashrate increases. HaPPYMine distributes rewards in proportion to expended hashrate and inherits the safety properties of the generalized proportional reward function established in [4]. We study HaPPYMine under a heterogeneous miner cost model and show that an equilibrium always exists with a unique set of miner participants and a unique total hashrate. Significantly, we prove that a HaPPYMine equilibrium is more decentralized than the static model equilibrium under a set of metrics including number of mining participants and hashrate distribution. Finally, we show that any HaPPYMine equilibrium is also safe against collusion and sybil attacks, and explore how the market value of the currency affects the equilibrium.

March 31 11AM ISEC 655 (inperson)/Zoom 
LaKyah Tyner Abstract Propertypreserving hashing (PPH) consists of a family of compressing hash functions h such that, for any two inputs x, y, we can correctly identify whether some property P(x, y) holds given only the digests h(x), h(y). In a basic PPH, correctness should hold with overwhelming probability over the choice of h when x, y are chosen apriori and independently of h, while in an adversarially robust PPH (RPPH), correctness must hold even when x, y are chosen adversarially and adaptively depending on h. Here, we study (R)PPH for the property that the Hamming distance between x and y is at most t. The notion of (R)PPH was introduced by Boyle, LaVigne and Vaikuntanathan (ITCS '19), and further studied by Fleischhacker, Simkin (Eurocrypt '21) and Fleischhacker, Larsen, Simkin (Eurocrypt'22). In this work, we obtain improved constructions that are conceptually simpler, have nearly optimal parameters, and rely on more general assumptions than prior works. Our results are:

March 24 11AM Zoom/ISEC 655 (screening) 
Hongyang Zhang Abstract We live in a society with vast amounts of information. New information content such as news articles, technical reports, short videos, and images are created on the Internet every day. These contents have led to the creation of many public datasets and (massive) deep neural networks trained on them. A broad research question is whether and how we can utilize numerous datasets and models to build better ML models. This requires rethinking the underlying algorithms and the learningtheoretic foundations. This talk will describe my lab's recent works towards addressing these questions. I will first describe the problem of transfer learning from pretrained deep neural networks and our approach to achieve robust transfer. Then, I will present a PACBayesian analysis of the generalization performance of our algorithm: The key idea being the measurement of Hessians. Lastly, I will talk about the problem of negative transfer in multitask learning. I will close my talk with ongoing and future directions about sharpness, distribution shifts, and building generalizable models across multiple tasks. 
Fall Semester, 2021
September 28 12PM ISEC 655 
Omri BenEliezer, MIT Abstract Streaming algorithms are traditionally divided into two categories: deterministic algorithms and randomized ones. These two types of algorithms exhibit a tradeoff between robustness and efficiency; on one hand, deterministic algorithms always return a correct output,
but for many important streaming problems, they are provably inefficient. On the other hand, efficient randomized algorithms are known for a very wide range of problems, but their correctness typically relies on the assumption that the stream is fixed in advance,
an assumption that is commonly unrealistic in practice. 
October 5 12PM ISEC 655 
Harm Derksen, NEU Abstract Suppose we are given a matrix whose entries depend linearly on some variables. Edmonds' problem from 1967 asks to find the rank of such a matrix over the field of rational functions. Plugging in random values for the variables gives a good probabilistic algorithm, but it is not known if there is a deterministic polynomial time algorithm for finding this rank. Surprisingly, there exists a deterministic polynomial time algorithm if the variables are not assumed to commute. This also leads to an interesting notion of noncommutative rank. I will discuss the commutative and noncommutative Edmonds' problem, and how work of Visu Makam and myself have contributed to this area. 
October 12 12PM ISEC 655 
Lydia Zakynthinou, NEU Abstract Covarianceaware mean estimation is a fundamental problem in statistics, where we are given n i.i.d. samples from a ddimensional distribution with mean $\mu$ and covariance $\Sigma$ and the goal is to find an estimator $\hat\mu$ with small error $\\hat\mu\mu\_{\Sigma}\leq \alpha$, where $\\cdot\_{\Sigma}$ denotes the Mahalanobis distance. It is known that the empirical mean of the dataset achieves this guarantee if we are given at least $n=\Omega(d/\alpha^2)$ samples. The empirical mean and other statistical estimators can reveal sensitive information about the samples of the training dataset. To protect the privacy of the individuals who participate in the dataset, we study statistical estimators which satisfy differential privacy, a condition that has become a standard criterion for individual privacy in statistics and machine learning. In this talk, I will present two new differentially private mean estimators for ddimensional (sub)Gaussian distributions with unknown covariance whose sample complexity is optimal up to logarithmic factors and matches the nonprivate one in many parameter regimes. All previous estimators with the same guarantee either require strong a priori bounds on the covariance matrix or require $\Omega(d^{3/2})$ samples. We will then focus on one of the estimators, which is based on a simple idea of perturbing the empirical mean of the dataset with noise calibrated to the empirical covariance, and we will explain the challenges and technical steps involved in making this estimator differentially private.

October 19 12PM ISEC 655 
William Kuszmaul, MIT Abstract The linearprobing hash table is one of the oldest and most widely used data structures in computer science. However, linear probing also famously comes with a major drawback: as soon as the hash table reaches a high memory utilization, elements within the hash table begin to cluster together, causing insertions to become slow. This phenomenon, now known as "primary clustering", was first captured by Donald Knuth in 1963; at a load factor of $1  1/x$, the expected time per insertion becomes $\Theta(x^2)$, rather than the more desirable $\Theta(x)$. We show that there is more to the story than the classic analysis would seem to suggest. It turns out that small design decisions in how deletions are implemented have dramatic effects on the asymptotic performance of insertions. If these design decisions are made correctly, then even a hash table that is continuously at a load factor $1  \Theta(1/x)$ can achieve average insertion time $\tilde{O}(x)$. A key insight is that the tombstones left behind by deletions cause a surprisingly strong "anticlustering" effect, and that when insertions and deletions are oneforone, the anticlustering effects of deletions actually overpower the clustering effects of insertions. We also present a new variant of linear probing, which we call "graveyard hashing", that completely eliminates primary clustering on any sequence of operations. If, when an operation is performed, the current load factor is $1  1/x$ for some $x$, then the expected cost of the operation is $O(x)$. One corollary is that, in the externalmemory model with a data block size of $B$, graveyard hashing offers the following remarkable guarantee: at any load factor $11/x$ satisfying $x = o(B)$, graveyard hashing achieves $1 + o(1)$ expected block transfers per operation. Past externalmemory hash tables have only been able to offer a $1+o(1)$ guarantee when the block size $B$ is at least $\Omega(x^2)$. Based on joint work with Michael A. Bender and Bradley C. Kuszmaul. https://arxiv.org/abs/2107.01250 To appear in FOCS 2021. 
October 26 12PM ISEC 655 
No talk scheduled 
November 2 12PM 
Konstantina Bairaktari, NEU Abstract A challenge in fair algorithm design is that, while there are compelling notions of individual fairness, these notions typically do not satisfy desirable
composition properties, and downstream applications based on fair classifiers might not preserve fairness. To study fairness under composition, Dwork and Ilvento (2019)
introduced an archetypal problem called faircohortselection problem, where a single fair classifier is composed with itself to select a group of candidates of a given size,
and proposed a solution to this problem.

November 9 12PM ISEC 655 
Peter Ivanov, NEU Abstract We study a simple and general template for constructing affine extractors by composing a linear transformation with resilient functions. Using this we show that good affine extractors can
be computed by nonexplicit circuits of various types, including AC0Xor circuits: AC0 circuits with a layer of parity gates at the input. We also show that onesided extractors can be
computed by small DNFXor circuits and separate these circuits from other wellstudied classes. As further motivation for studying DNFXor circuits we show that if they can approximate
inner product then small AC0Xor circuits can compute it exactly – a longstanding open problem.

November 16 12PM ISEC 655 
Maryam Aliakbarpour, BU+NEU Abstract In this talk, we present a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. The main motivation
for considering this setting is that it captures data collection in the real world. We explain a brief description of our testers for the following problems in this setting when given
samples from s distributions, p_1, p_2, . . . , p_s: (1) Uniformity Testing: Testing whether all the p_i’s are uniform or epsfar from being uniform in \ell_1distance (2) Identity Testing:
Testing whether all the p_i’s are equal to an explicitly given distribution q or epsfar from q in \ell_1distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a
distribution q which we have sample access to, or epsfar from q in \ell_1distance. By assuming an additional natural condition about the source distributions, we provide sample optimal
testers for all of these problems.

November 23 12PM ISEC 655 
Willy Quach, NEU Abstract The talk will be about socalled lossy functions, a family of cryptographic primitives that has found a wide variety of applications. While the original notion of lossy trapdoor functions,
introduced by Peikert and Waters (STOC '08), have now found countless applications, they are a relatively higherend primitive that can only be built from ``publickey'' computational assumptions.
In this work, we define and explore a relaxation that we call targeted lossy functions. We show that such a relaxation is meaningful by (1) building it from substantially weaker assumptions
(namely oneway functions and variants) and (2) showing several applications.

November 30 12PM ISEC 655 
Chara Podimata, Harvard Abstract
We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as featurebased dynamic pricing. Standard gametheoretic formulations of this
problem assume that agents act in accordance with a specific behavioral model. In practice, however, some agents may not subscribe to the dominant behavioral model or may act in ways that seem
to be arbitrarily irrational. Existing algorithms heavily depend on the behavioral model being (approximately) accurate for all agents and have poor performance in the presence of even a few such
arbitrarily irrational agents. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying behavioral model. In particular, we provide
two algorithms, one based on multidimensional binary search methods, and one based on gradient descent. We show that these algorithms attain nearoptimal regret guarantees in the absence of
irrational agents and their performance degrades gracefully with the number of such agents, providing the first results for contextual search in any adversarial noise model. Our techniques
draw inspiration from learning theory, game theory, highdimensional geometry, and convex analysis.

December 7 12PM ISEC 655 
Benjamin Lovitz, U. Waterloo Abstract Tensors are natural generalizations of matrices to higherway arrays. Decompositions of tensors into sums of product (rankone) tensors are useful in many areas for compressing
and interpreting the information stored in a tensor. The tensor rank, which naturally generalizes matrix rank, is the smallest number of product tensors that can decompose a
given tensor. In contrast to matrices, tensor rank decompositions are often unique (up to trivialities). Uniqueness is useful in applications, as it corresponds to a unique
interpretation of the information stored in a tensor. I will review a concrete application of uniqueness in unsupervised learning. 
Spring Semester, 2020
February 5 
Jinshuo Dong, UPenn Abstract It is important to understand the exact privacy guarantee provided by private algorithms developed in the past prosperous decade of differential privacy. In particular, any underestimation of actual privacy means unnecessary noise in the algorithm and loss in the final accuracy. We observe a central limit behavior in iterative private algorithms, which demonstrates the limit of the common $(\varepsilon,\delta)$ parametrization in most application scenarios. For the rescue, a new notion called Gaussian Differential Privacy (GDP) is proposed and a complete toolkit is developed. We carry out various experiments to show how much unnecessary loss of accuracy can be saved in deep learning applications. Based on joint work with Aaron Roth, Weijie Su, Zhiqi Bu and Qi Long. 
February 12 12:30PM ISEC 655 
Shibani Santurkar, MIT Abstract We present a new perspective on the phenomenon of widespread vulnerability of current machine learning models to adversarial examples. Specifically, we discuss how the existence of adversarial examples stems, in large part, from a fundamental misalignment in the way humans and machine learning models solve classification tasks. This view also brings to light some benefits of robust models—such as their ability to learn representations that are more humanaligned. Overall, this perspective highlights the utility of adversarial robustness as a goal beyond the security context. 
February 19 12:30PM ISEC 655 
Ramesh Krishnan S. Pallavoor, Boston University Abstract We study the problem of approximating the distance to monotonicity of Boolean functions over the hypercube domain. For a function f:{0,1}^n > {0,1}, the distance to monotonicity of f is the minimum fraction of points at which f has to be modified to make it monotone. We give a nonadaptive algorithm that, given f:{0,1}^n > {0,1} whose distance to monotonicity is at least \alpha, makes poly(n, 1/\alpha) queries and returns an O(\sqrt{n} polylog n)multiplicative approximation to the distance to monotonicity of f. Furthermore, we show that for any constant k > 0, approximating the distance to monotonicity up to n^{0.5  k}factor requires 2^{n^k} nonadaptive queries, thereby ruling out a poly(n, 1/\alpha)query nonadaptive algorithm for such approximations. This answers a question of Seshadhri (Property Testing Review ’14) for the case of nonadaptive algorithms. Approximating the distance to a property is equivalent to tolerantly testing that property. Our lower bound stands in contrast to standard (nontolerant) testing of monotonicity that can be done nonadaptively with O(\sqrt{n} polylog n) queries. We obtain our lower bound by proving an analogous bound for erasureresilient testers. Our method yields the same lower bounds for other properties (unateness and being a kjunta). These lower bounds improve exponentially on the existing lower bounds for these properties. This talk is based on a joint work with Sofya Raskhodnikova and Erik Waingarten that appeared in SODA 2020. 
February 26 12:30PM ISEC 655 
Gabrielle De Micheli, INRIA Abstract The discrete logarithm problem is one of the two hard mathematical problems at the foundation of today's public key cryptography. In this presentation, I will talk about the discrete logarithm problem at the boundary case between small and medium characteristic finite fields, which is precisely the area where finite fields used in pairingbased cryptosystems live. In order to evaluate the security of pairingbased protocols, we thoroughly analyze the complexity of all the algorithms that coexist at this boundary case: the QuasiPolynomial algorithms, the Number Field Sieve and its many variants, and the Function Field Sieve. We adapt the latter to the particular case where the extension degree is composite, and show how to lower the complexity by working in a shifted function field. All this study finally allows us to give precise values for the characteristic asymptotically achieving the highest security level for pairings. 
Fall Semester, 2019
October 2 1:30PM ISEC 655 
Tanay Mehta, Northeastern University Abstract Consider the query reformulation problem where a user enters the shopping query “anxiety toy rotating” into an ecommerce website. This query has no textual similarity to “fidget spinners” which is, in fact, the product the user is looking for. Traditionally, such language processing tasks are tackled using memorybased architectures (LSTMs). We solve the problem of query reformulation by adopting a first principles approach. We propose a simple theoretical model of query generation, AttEST, that views both products and ngrams as vectors embedded in a latent attribute space. We realize a practical implementation of AttEST as a feedforward neural network with an attention mechanism. The AttEST network beats the memorybased architectures by over 20 percentage points (on the F1 score). We explain this outperformance by giving a theoretical justification for attention as the best linear unbiased estimator. Joint work with M. Dippel, A. Kiezun, R. Sundaram, S. Thirumalai and A. Varma 
October 9 12:00PM ISEC 655 
Mark Bun, Boston University Abstract We investigate the problem of differentially private hypothesis selection: Given i.i.d. samples from an unknown probability distribution P and a set of m probability distributions H, the goal is to privately output a distribution from H whose total variation distance to P is comparable to that of the best such distribution. We present several algorithms for this problem which achieve sample complexity similar to those of the best nonprivate algorithms. These give new and improved learning algorithms for a number of natural distribution classes. Our results also separate the sample complexities of private mean estimation under product vs. nonproduct distributions. 
October 16 12:00PM ISEC 655 
Talya Eden, MIT Abstract In this talk, I will discuss the problem of sampling edges in an unknown graph G = (V,E) from a distribution that is pointwise almost uniform over E. Given query access to a graph G over n vertices, m edges and a bound on the arboricity of G, I will describe an algorithm that performs queries in expectations and returns an edge in the graph such that every edge is sampled with probability . We also show that the upper bound is tight (up to polylogarithmic factors and the dependence in ). If time will permit I will also discuss a simple algorithm for estimating the number of edges in graphs with bounded arboricity. This talk is based on joint work with Dana Ron and Will Rosenbaum. 
October 23 12:00PM ISEC 655 
Archita Agarwal, Brown University Abstract Distributed hash tables (DHT) are a fundamental building block in the design of distributed systems with applications ranging from content distribution networks to offchain storage networks for blockchains and smart contracts. When DHTs are used to store sensitive information, system designers use endtoend encryption to guarantee the confidentiality of their data. A prominent example is Ethereum’s offchain network Swarm. In this work, we formalize the use of endtoend encryption in DHTs and the many systems they support. We introduce the notion of an encrypted DHT and provide simulationbased security definitions that capture the security properties one would desire from such a system. Using our definitions, we then analyze the security of a standard approach to storing encrypted data in DHTs. Interestingly, we show that this “standard scheme” leaks information probabilistically, where the probability is a function of how well the underlying DHT load balances its data. We also show that to be securely used with the standard scheme, a DHT needs to satisfy a form of equivocation with respect to its overlay. To show that these properties are indeed achievable in practice, we study the balancing properties of the Chord DHT—arguably the most influential DHT—and show that it is equivocable with respect to its overlay in the random oracle model. Finally, we consider the problem of encrypted DHTs in the context of transient networks, where nodes are allowed to leave and join. 
October 30 12:00PM ISEC 655 
Nishanth Dikkala, MIT Abstract Statistical learning theory has largely focused on learning and generalization given independent and identically distributed samples. Motivated by settings where data is sampled on a network or a spatial domain, we provide learning and generalization bounds for data that are complexly dependent, yet their distribution satisfies the Dobrushin’s condition. Indeed, we show that the standard complexity measures of Gaussian and Rademacher complexities and VC dimension are sufficient measures of complexity for the purposes of bounding the generalization error and learning rates of hypothesis classes in our setting. Moreover, our generalization bounds only degrade by constant factors compared to their i.i.d. analogs, and our learnability bounds degrade by log factors in the size of the training set. This is joint work with my advisor Costis Daskalakis, Yuval Dagan and Siddhartha Jayanti. 
November 6 12:00PM ISEC 655 
Tal Wagner, MIT Abstract We prove tight bounds on the bit complexity of approximately representing an npoint Euclidean metric space. We show that bits are both sufficient and necessary for recovering each distance up to distortion , where is the aspect ratio of the metric space (ratio of largest to smallest distance). This improves over the bound which follows from the dimension reduction theorem of Johnson and Lindenstrauss (1984), and by over a previous result of the authors (SODA 2017). In words, while the dimension reduction theorem states that each point can be represented by coordinates, we show it can be represented by that many bits. Joint work with Piotr Indyk. 
November 13 12:00PM ISEC 655 
Chara Podimata, Harvard University Abstract We study the problem of online learning in strategic classification settings from the perspective of the learner, who is repeatedly facing myopically rational strategic agents. We model this interplay as a repeated Stackelberg game, where at each timestep the learner deploys a highdimensional linear classifier first and an agent, after observing the classifier, along with his real feature vector, and according to his underlying utility function, bestresponds with a (potentially altered) feature vector. We measure the performance of the learner in terms of Stackelberg regret for her 01 loss function. Surprisingly, we prove that in strategic settings like the one considered in this paper there exist worstcase scenarios, where any sequence of actions providing sublinear external regret might result in linear Stackelberg regret and vice versa. We then provide the Grinder Algorithm, an adaptive discretization algorithm, potentially of independent interest in the online learning community, and prove its datadependent upper bound on the Stackelberg regret given oracle access, while being computationally efficient. We also provide a nearly matching lower bound for the problem of strategic classification. We complement our theoretical analysis with simulation results, which suggest that our algorithm outperforms the benchmarks, even given access to approximation oracles. Our results advance the known stateoftheart results in the growing literature of online learning from revealed preferences, which has so far focused on “smoother” utility and loss functions from the perspective of the agents and the learner respectively. Joint work with Yiling Chen and Yang Liu 
December 4 12:00PM ISEC 655 
Katerina Sotiraki, MIT Abstract We study the search problem class PPA_{q} defined as a moduloq analog of the wellknown polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_{p} for prime p. Our main result is to establish that an explicit version of a search problem associated to the Chevalley–Warning theorem is complete for PPA_{p} for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA_{p} when p ≥ 3. We also discuss connections between ChevalleyWarning theorem and the wellstudied short integer solution problem and survey the structural properties of PPA_{q}. Joint work with Mika Göös, Pritish Kamath and Manolis Zampetakis 
December 11 12:00PM ISEC 655 
Josh Alman, Harvard University Abstract We study the known techniques for designing Matrix Multiplication algorithms. The two main approaches are the Laser method of Strassen, and the Group theoretic approach of Cohn and Umans. We define a generalization based on restrictions of powers of tensors which subsumes these two approaches, which we call the Universal method. We then prove concrete lower bounds on the algorithms one can design by applying the Universal method to many different tensors. Our proofs use new tools for upper bounding the asymptotic slice rank of a wide range of tensors. Our main result is that the Universal method applied to any CoppersmithWinograd tensor (the family of tensors used in all recordholding algorithms from the past 30+ years) cannot yield a bound on omega, the exponent of matrix multiplication, better than 2.16805. No background knowledge about matrix multiplication algorithms is assumed. Some of the talk is based on joint work with Virginia Vassilevska Williams. 
Spring Semester, 2019
January 30 1:00PM WVH 366 
Hugo Alves Akitaya, Tufts University Abstract An embedding of a graph $G$ is a drawing $\varphi:G\rightarrow M$ of $G$ on a surface $M$ such that every point each vertex in $V(G)$ is mapped to distinct points and each edge in $E(G)$ to interiordisjoint Jordan arcs between the corresponding vertices. A weak embedding is a map $\varphi:G\rightarrow M$ if, for every $\epsilon>0$, there exist an embedding $\psi_\epsilon:G\rightarrow M$ so that $\\varphi\psi_\epsilon\<\epsilon$, where $\.\$ is the uniform norm (i.e., $\sup$ norm). We say that the embedding $\psi_{\varphi}$ approximates $\varphi$. The study of weak embeddings lies at the interface of several independent lines of research in mathematics and computer science. In particular, it generalizes various graph visualization models and is a special case of the notoriously difficult clusterplanarity problem. It is also related to the foldability problem in computational origami. This talk presents several results on the algorithmic complexity of recognizing weak embeddings. 
February 13 1:00PM WVH 366 
Paul Hand, Northeastern University Abstract Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct lowdimensional parameterizations of the manifold of images or signals belonging to a particular natural class, allowing for recovery algorithms to be posed in a lowdimensional space. This dimensionality may even be lower than the sparsity level of the same signals when viewed in a fixed basis. In this talk, we will show rigorous recovery guarantees for solving inverse problems under a learned generative prior. First, we will discuss convergence guarantees for compressive sensing under random neural network priors. Then, we will show that generative priors allow for a significant advance to be made in the problem of compressive phase retrieval. To date, no known computationally efficient algorithm exists for solving phase retrieval under a sparsity prior at sample complexity proportional to the signal complexity. With generative priors, we establish a new approach for compressive phase retrieval and establish rigorous guarantees with sample complexity proportional to the signal complexity. 
February 20 1:00PM WVH 366 
Ram Ramanathan, Chief Scientist, goTenna Abstract Decentralized infrastructureless wireless networks can provide instantlydeployable and robust connectivity in the aftermath of natural disasters, in remote areas, and in other contexts such as the InternetofThings. After briefly introducing goTenna and multihop wireless networking, I will discuss the tradeoffs involved in designing such networks focusing in particular on connectivity properties using insights from percolation theory. I will then consider one particular problem, namely networkwide packet broadcasting, which is closely related to the Connected Dominating Set problem in graphs. I will present a fully distributed zerocontrol protocol for broadcasting and discuss its correctness and performance. Finally, I will touch upon some research challenges in the area such as incentivizing network growth using cryptocurrencies. 
February 27 1:00PM WVH 366 
Jarosław Błasiok, Harvard University Abstract The distinct elements problem is one of the fundamental problems in streaming algorithms  given a stream of integers in the range $\{1,\ldots,n\}$, we wish to provide a $(1+\varepsilon)$ approximation to the number of distinct elements in the input. After a long line of research optimal solution for this problem with constant probability of success, using $\mathcal{O}(\frac{1}{\varepsilon^2}+\log n)$ bits of space, was given by Kane, Nelson and Woodruff in 2010. The standard approach used in order to achieve low failure probability $\delta$, is to take a median of $\log \delta^{1}$ parallel repetitions of the original algorithm and report the median of computed answers. We show that such a multiplicative space blowup is unnecessary: we provide an optimal algorithm using $\mathcal{O}(\frac{\log \delta^{1}}{\varepsilon^2} + \log n)$ bits of space  matching known lower bounds for this problem. That is, the $\log\delta^{1}$ factor does not multiply the $\log n$ term. This settles completely the space complexity of the distinct elements problem with respect to all standard parameters. We consider also \emph{strong tracking} (or \emph{continuous monitoring}) variant of the distinct elements problem, where we want an algorithm which provides an approximation of the number of distinct elements seen so far, at all times of the stream. We show that this variant can be solved using $\mathcal{O}(\frac{\log \log n + \log \delta^{1}}{\varepsilon^2} + \log n)$ bits of space, which we show to be optimal. 
March 27 1:00PM WVH 366 
Christina Ilvento, Harvard University Abstract There has been much discussion recently about how fairness should be measured or enforced in classification. Individual Fairness [Dwork et al. 2012], which requires that similar individuals be treated similarly, is a highly appealing definition because it gives very strong guarantees on treatment of individuals. Unfortunately, the need for a taskspecific similarity metric has prevented its use in practice. In this work, we set out a framework for approximating a metric for Individual Fairness based on human judgements. Our model assumes that we have access to a human fairness arbiter, who can answer a limited set of queries concerning similarity of individuals for a particular task, is free of explicit biases and possesses sufficient domain knowledge to evaluate similarity. Our contributions include useful definitions for metric approximation relevant for Individual Fairness, constructions for approximations from a limited number of realistic queries to the arbiter on a fixed sample of individuals, and learning procedures to construct hypotheses for metric approximations which generalize to unseen samples under certain assumptions of learnability of distance threshold functions. 
April 10 1:00PM WVH 366 
Oxana Poburinnaya, Boston University Abstract While standard encryption guarantees secrecy of the encrypted plaintext only against an attacker that has no knowledge of the communicating parties’ keys and randomness of encryption, deniable encryption [Canetti et al., Crypto’96] provides the additional guarantee that the plaintext remains secret even in face of entities that attempt to coerce (or bribe) the communicating parties to expose their internal states, including the plaintexts, keys and randomness. To achieve this guarantee, deniable encryption equips the parties with faking algorithms which allow them to generate fake keys and randomness that make the ciphertext appear consistent with any plaintext of the parties’ choice. To date, however, only partial results were known: Either deniability against coercing only the sender, or against coercing only the receiver [SahaiWaters, STOC ‘14] or schemes satisfying weaker notions of deniability [O’Neil et al., Crypto ‘11]. In this paper we present the first fully bideniable interactive encryption scheme, thus resolving the 20yearsold open problem. Our scheme also provides an additional and new guarantee: Even if the sender claims that one plaintext was used and the receiver claims a different one, the adversary has no way of figuring out who is lying  the sender, the receiver, or both. This property, which we call offtherecord deniability, is useful when the parties don’t have means to agree on what fake plaintext to claim, or when one party defects against the other. Our protocol has three messages, which is optimal [Bendlin et al., Asiacrypt’11], and needs a globally available reference string. We assume subexponential indistinguishability obfuscation (IO) and oneway functions. Joint work with Ran Canetti and Sunoo Park 
April 17 1:00PM ISEC 655 
Dimitris Tsipras, MIT Abstract Recent progress in machine learning has made the deployment of ML systems in the real world an imminent possibility. But are our current machine learning systems really up to the task? In this talk, I will discuss the brittleness and vulnerability of the existing ML toolkit. I will then describe a conceptual framework that aims to deliver models that are more reliable, and robust to adversarial manipulation. Finally, I will outline how this framework constitutes a new learning paradigm, how it differs from the classic perspective, and what new challenges it gives rise to. 
April 24 1:00PM WVH 366 
Mitali Bafna, Harvard University Abstract In the last several years, neural networks have made unprecedented achievements on computational learning tasks like image classification. Despite their remarkable success, neural networks have been shown to be brittle in the presence of adversarial noise. Many effective attacks have been proposed in the context of computer vision that reliably generate small perturbations to input images (sometimes imperceptible to humans) that drastically change the network’s classification of the image. In this work, we give a framework for improving the robustness of classifiers to adversaries with L_0 noise budgets. That is, adversaries are restricted in the number of features they can corrupt, but may corrupt each arbitrarily. Our framework is based on a new Sparse Discrete Fourier transform (DFT) that is robust to worstcase L_0 noise added in the time domain. We give a new algorithm for approximating the DFT of an approximately sparse signal that has been corrupted by worstcase L_0 noise, namely a bounded number of coordinates of the signal have been corrupted arbitrarily. Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their highdimensional analogs. We use our algorithm to successfully defend against well known L_0 adversaries in the setting of image classification. We give experimental results on the Jacobianbased Saliency Map Attack (JSMA) and the Carlini Wagner (CW) L_0 attack on the MNIST and FashionMNIST datasets as well as the Adversarial Patch on the ImageNet dataset. 
Fall Semester, 2018
September 13 12:00PM 150 Forsyth 
Eylon Yogev, Weizmann Institute of Science Abstract The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one of the main research objectives in the context of TFNP is to search for efficient algorithms for its subclasses, and at the same time proving hardness results where efficient algorithms cannot exist. Currently, no problem in TFNP is known to be hard under assumptions such as NP hardness, the existence of oneway functions, or even publickey cryptography. The only known hardness results are based on less general assumptions such as the existence of collisionresistant hash functions, oneway permutations less established cryptographic primitives (e.g. program obfuscation or functional encryption). Several works explained this status by showing various barriers to proving hardness of TFNP. In particular, it has been shown that hardness of TFNP hardness cannot be based on worstcase NP hardness, unless NP=coNP. Therefore, we ask the following question: What is the weakest assumption sufficient for showing hardness in TFNP? In this talk, I will answer this question and show that hardonaverage TFNP problems can be based on the weak assumption that there exists a hardonaverage language in NP. In particular, this includes the assumption of the existence of oneway functions. In terms of techniques, there is an interesting interplay between problems in TFNP and derandomization techniques. Based on joint works with Pavel Hubáček, and Moni Nao 
September 20 12:00PM 150 Forsyth 
Alina Ene, Boston University Abstract In this talk, we present recent progress on understanding the tradeoff between the approximation guarantee and adaptivity for submodular maximization. The adaptivity of an algorithm is the number of sequential rounds of queries it makes to the evaluation oracle of the function, where in every round the algorithm is allowed to make polynomiallymany parallel queries. Adaptivity is an important consideration in settings where the objective function is estimated using samples and in applications where adaptivity is the main running time bottleneck. We present nearlyoptimal algorithms for submodular maximization subject to a cardinality constraint and more generally, subject to multiple packing constraints. This talk is based on joint work with Huy Nguyen (Northeastern) and Adrian Vladu (Boston University). 
September 27 12:00PM 655 ISEC 
Lucianna Kiffer (internal) Abstract The celebrated Nakamoto consensus protocol ushered in several new consensus applications including cryptocurrencies. A few recent works have analyzed important properties of blockchains, including most significantly, consistency, which is a guarantee that all honest parties output the same sequence of blocks throughout the execution of the protocol. To establish consistency, the prior analysis of Pass, Seeman and shelat required a careful counting of certain combinatorial events that was difficult to apply to variations of Nakamoto. Work by Garay, Kiayas, and Leonardas provides another method of analyzing the blockchain under the simplifying assumption that the network was synchronous. The contribution of this paper is the development of a simple Markovchain based method for analyzing consistency properties of blockchain protocols. The method includes a formal way of stating strong concentration bounds as well as easy ways to concretely compute the bounds. We use our new method to answer a number of basic questions about consistency of blockchains:
In each case, we use our framework to experimentally analyze the consensus bounds for various network delay parameters and adversarial computing percentages. We hope our techniques enable authors of future blockchain proposals to provide a more rigorous analysis of their schemes. 
October 4 12:00PM 150 Forsyth 
Maryam Aliakbarpour, MIT Abstract In this talk, we will discuss new directions in testing properties of distributions. Distributions are at the core of datarelated scientific endeavors, and due to their importance, they have been studied for past decades in Statistics and Computer Science. The goal is to find an algorithm to test the properties of distributions with provable performance guarantees, using as few samples as possible. We discuss the fundamental problems of identity (goodness of fit) and closeness (equivalence) testing concerning the new challenges:

October 11 12:00PM 150 Forsyth 
Tanay Mehta (internal) Abstract We propose a new model for the study of resilience of coevolving multiplex scalefree networks. Our network model, called preferential interdependent networks, is a novel continuum over scalefree networks parameterized by their correlation ρ, 0 ≤ ρ ≤ 1. Our failure and recovery model ties the propensity of a node, both to fail and to assist in recovery, to its importance. We show, analytically, that our network model can achieve any γ,2 ≤ γ ≤ 3 for the exponent of the power law of the degree distribution; this is superior to existing multiplex models and allows us better fidelity in representing realworld networks. Our failure and recovery model is also a departure from the much studied cascading error model based on the giant component; it allows for surviving important nodes to send assistance to the damaged nodes to enable their recovery. This better reflects the reality of recovery in manmade networks such as social networks and infrastructure networks. Our main finding, based on simulations, is that resilient preferential interdependent networks are those in which the layers are neither completely correlated (ρ = 1) nor completely uncorrelated (ρ = 0) but instead semicorrelated (ρ ≈ 0.1 − 0.3). This finding is consistent with the realworld experience where complex manmade networks typically bounce back quickly from stress. In an attempt to explain our intriguing empirical discovery we present an argument for why semicorrelated multiplex networks can be the most resilient. Our argument can be seen as an explanation of plausibility or as an incomplete mathematical proof subject to certain technical conjectures that we make explicit. Joint work with Auroop Ganguly, Ravi Sundaram and Devesh Tiwari 
October 18 12:00PM 655 ISEC 
Manolis Zampetakis, MIT Abstract We consider the classical statistical problem of estimating to arbitrary accuracy the parameters of a multidimensional Gaussian distribution under the following realworld obstacles: (1) truncated samples, (2) inhomogeneous population.
Abstracting the use of iterative algorithms in the previous important statistical problems, we consider the general question of analyzing the convergence of iterative algorithms. We prove that contraction maps provide a universal analysis tool for proving global convergence of iterative maps. Based on joint works with: Constantinos Daskalakis, Themis Gouleakis and Christos Tzamos. 
November 1 12:00PM 655 ISEC 
Ran Cohen (internal) Abstract Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) Where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) Where edges in the communication graph are determined dynamically as part of the protocol. Whereas a rich literature has succeeded in mapping out the feasibility and limitations of graph structures supporting secure computation in the fixedgraph model (including strong classical lower bounds), these bounds do not apply in the latter dynamicgraph setting, which has recently seen exciting new results, but remains relatively unexplored. In this work, we initiate a similar foundational study of MPC within the dynamicgraph model. As a first step, we investigate the property of graph expansion. All existing protocols (implicitly or explicitly) yield communication graphs which are expanders, but it is not clear whether this is inherent. Our results consist of two types (for constant fraction of corruptions):
More generally, we provide a formal framework for analyzing the evolving communication graph of MPC protocols, giving a starting point for studying the relation between secure computation and further, more general graph properties. 
November 8 12:00PM 655 ISEC 
Seth Neel, University of Pennsylvania Abstract We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However, privacy guarantees cannot be evaluated empirically, and must be proven — without making heuristic assumptions. We show that learning problems over broad classes of functions — those that have polynomially sized universal identification sets — can be solved privately and efficiently, assuming the existence of a nonprivate oracle for solving the same problem. Our first algorithm yields a privacy guarantee that is contingent on the correctness of the oracle. We then give a reduction which applies to a class of heuristics which we call certifiable, which allows us to convert oracledependent privacy guarantees to worstcase privacy guarantee that hold even when the heuristic standing in for the oracle might fail in adversarial ways. Finally, we consider classes of functions for which both they and their dual classes have small universal identification sets. This includes most classes of simple boolean functions studied in the PAC learning literature, including conjunctions, disjunctions, parities, and discrete halfspaces. We show that there is an efficient algorithm for privately constructing synthetic data for any such class, given a non private learning oracle. This in particular gives the first oracleefficient algorithm for privately generating synthetic data for contingency tables. The most intriguing question left open by our work is whether or not every problem that can be solved differentially privately can be privately solved with an oracleefficient algorithm. While we do not resolve this, we give a barrier result that suggests that any generic oracleefficient reduction must fall outside of a natural class of algorithms (which includes the algorithms given in this paper). 
November 15 12:00PM 655 ISEC 
Albert Cheu (internal) Abstract We consider the problem of designing scalable, robust protocols for computing statistics about sensitive data. Specifically, we look at how best to design differentially private protocols in a distributed setting, where each user holds a private datum. The literature has mostly considered two models: the “central” model, in which a trusted server collects users’ data in the clear, which allows greater accuracy; and the “local” model, in which users individually randomize their data, and need not trust the server, but accuracy is limited. Attempts to achieve the accuracy of the central model without a trusted server have so far focused on variants of cryptographic MPC, which limits scalability. In this paper, we initiate the analytic study of a shuffled model for distributed differentially private algorithms, which lies between the local and central models. This simpletoimplement model, a special case of the ESA framework of [Bittau et al., '17], augments the local model with an anonymous channel that randomly permutes a set of usersupplied messages. For sum queries, we show that this model provides the power of the central model while avoiding the need to trust a central server and the complexity of cryptographic secure function evaluation. More generally, we give evidence that the power of the shuffled model lies strictly between those of the central and local models: for a natural restriction of the model, we show that shuffled protocols for a widely studied selection problem require exponentially higher sample complexity than do centralmodel protocols. 
November 29 12:00PM 655 ISEC 
Ilias Zadik, MIT Abstract Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the socalled nodedifferentially private algorithms, which compute information about a graph or network while provably revealing almost no information about the presence or absence of a particular node in the graph. We provide new algorithms for nodedifferentially private estimation for a popular and expressive family of network models: stochastic block models and their generalization, graphons. Our algorithms improve on prior work reducing their error quadratically and matching, in many regimes, the optimal nonprivate algorithm. We also show that for the simplest random graph models (G(n, p) and G(n, m)), nodeprivate algorithms can be qualitatively more accurate than for more complex models—converging at a rate of $1 / \epsilon^2 n^3$ instead of $1 / \epsilon^2 n^2$. This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful. 
December 13 12:00PM 655 ISEC 
Alexander Russell, University of Connecticut Abstract Bitcoin has ushered in a new era of interest in cryptocurrencies and distributed algorithms for consensus. While Bitcoin provides a spectacular solution in this space, it uses a "proofofwork" mechanism that makes quite awesome resource demands: the protocol is projected to burn approximately 70TWh next year, as much as the country of Austria. Proofofstake is an alternative framework that has the potential to remove these energy demands. However, proofofstake protocols face numerous analytic challenges that do not exist in the proofofwork setting. We will begin with an overview of the Bitcoin system, focusing on the proofofwork mechanism. We will then describe the constructions and analyses of the Ouroboros blockchains, the first blockchain protocols providing provable security in the proofofstake setting. These new blockchains are now deployed as a part of the Cardano/ADA cryptocurrency. The analysis shows off a number of new analytic features of interest and makes connections to coupled Markov chains, combinatorics, and the UCmodel of protocol security. This is joint work with Bernardo David, Aggelos Kiayias, Peter Gazi, and Roman Oliynikov. 
Spring Semester, 2018
Jan 16, 2018 3:30PM 
Steven Wu, MSR 142 ISEC Abstract Bandit learning is characterized by the tension between longterm exploration and shortterm exploitation. However, as has recently been noted, in settings in which the choices of the learning algorithm correspond to important decisions about individual people (such as criminal recidivism prediction, lending, and sequential drug trials), exploration corresponds to explicitly sacrificing the wellbeing of one individual for the potential future benefit of others. This raises a fairness concern. In such settings, one might like to run a “greedy” algorithm, which always makes the (myopically) optimal decision for the individuals at hand — but doing this can result in a catastrophic failure to learn. In this paper, we consider the linear contextual bandit problem and revisit the performance of the greedy algorithm. We give a smoothed analysis, showing that even when contexts may be chosen by an adversary, small perturbations of the adversary’s choices suffice for the algorithm to achieve “no regret”, perhaps (depending on the specifics of the setting) with a constant amount of initial training data. This suggests that “generically” (i.e. in slightly perturbed environments), exploration and exploitation need not be in conflict in the linear setting. 
Jan 23, 2018 3:30PM 
Michael Mitzenmacher 142 ISEC Abstract We present cuckoo filters, an efficient data structure for approximate set membership that improves on the wellknown Bloom filter. We then discuss recent work on how to make cuckoo filters adaptive in response to false positives, which can be important for many practical problems. 
Jan 30, 2018 3:30PM 
Audra McMillan, University of Michigan 142 ISEC Abstract Physical sensors (thermal, light, motion, etc.) are becoming ubiquitous and offer important benefits to society. However, allowing sensors into our private spaces has resulted in considerable privacy concerns. Differential privacy has been developed to help alleviate these privacy concerns. In this talk, we’ll develop and define a framework for releasing physical data that preserves both utility and provides privacy. Our notion of closeness of physical data will be defined via the Earth Mover Distance and we’ll discuss the implications of this choice. Physical data, such as temperature distributions, are often only accessible to us via a linear transformation of the data. We’ll analyse the implications of our privacy definition for linear inverse problems, focusing on those that are traditionally considered to be "illconditioned”. We’ll then instantiate our framework with the heat kernel on graphs and discuss how the privacy parameter relates to the connectivity of the graph. Our work indicates that it is possible to produce locally private sensor measurements that both keep the exact locations of the heat sources private and permit recovery of the ``general geographic vicinity'' of the sources. Joint work with Anna C. Gilbert. 
Feb 13, 2018 3:30PM 
Jack Doerner, Northeastern University 142 ISEC Abstract We design and implement a Distributed Oblivious Random Access Memory (DORAM) data structure that is optimized for use in twoparty secure computation protocols. We improve upon the access time of previous constructions by a factor of up to ten, their memory overhead by a factor of one hundred or more, and their initialization time by a factor of thousands. We are able to instantiate ORAMs that hold 2^34 bytes, and perform operations on them in seconds, which was not previously feasible with any implemented scheme. Unlike prior ORAM constructions based on hierarchical hashing, permutation, or trees, our Distributed ORAM is derived from the new Function Secret Sharing scheme introduced by Boyle, Gilboa and Ishai. This significantly reduces the amount of secure computation required to implement an ORAM access, albeit at the cost of O(n) efficient local memory operations. We implement our construction and find that, despite its poor O(n) asymptotic complexity, it still outperforms the fastest previously known constructions, Circuit ORAM and Squareroot ORAM, for datasets that are 32 KiB or larger, and outperforms prior work on applications such as stable matching or binary search by factors of two to ten. 
Feb 27, 2018 3:30PM 
Albert Cheu, Northeastern University 142 ISEC Abstract The multiarmed bandit setting is a wellstudied learning model. Within this setting, the approximate best arm identification problem has been solved optimally, using a clever technique to avoid a union bound. In our work, we pose a variant problem and present an optimal algorithm, which also avoids a union bound. We give intuition for the solution and, time permitting, the matching impossibility result. Joint work with Ravi Sundaram and Jonathan Ullman. 
March 20, 2018 3:30PM 
Ryan Williams 142 ISEC Abstract I will give an overview of the recent proof (with my PhD student Cody Murray) that the class NQP = NTIME\((n^{polylog n})\) does not have ACC circuits of \(n^{log n}\) size (even with a layer of threshold gates at the bottom). This is achieved by strengthening a key component of the proof of NEXP not in ACC; in particular, we prove a new "Easy Witness Lemma" for NQP. 
March 27, 2018 3:30PM 
Nithin Varma, Boston University 142 ISEC Abstract Property testing is a formal framework to design algorithms for large datasets. The traditional definition of property testing [Rubinfeld & Sudan '96, Goldreich, Goldwasser & Ron '98] abstracts datasets as functions and assumes that an algorithm (also called tester) can query points in the domain of a function to obtain the corresponding values. The task of the tester is to distinguish, with probability 2/3, between the case that the function f being queried belongs to a set (property) P and the case that f is `far' from every function in P, for an appropriate measure of distance. One of the key assumptions in the above definition, that the tester has access to function values at all of the queried domain points, is not applicable to most reallife datasets. It could be the case that some or several of the function values are kept hidden for privacy reasons, or erased by mistake or by an adversary. Querying such erased points does not provide an algorithm with any information about the function. Moreover, it might happen that, an algorithm, by not knowing the locations of these erasures, makes a lot of queries to erased points and turns out entirely useless. In the talk, I will describe the erasureresilient property testing model that we defined to account for the occurrence of erasures in datasets. We will then present and analyse our erasureresilient tester for monotonicity of functions. Joint work with Kashyap Dixit, Sofya Raskhodnikova and Abhradeep Thakurta. 
April 3, 2018 3:30PM 
Aanchal Malhotra, Boston University 142 ISEC Abstract The security of almost any realworld distributed system today depends on the participants having some "reasonably accurate" sense of current real time. Indeed, to name one example, the very authenticity of practically any communication on the Internet today hinges on the ability of the parties to accurately detect revocation of certificates, or expiration of passwords or shared keys. However, as recent attacks show, the standard protocols for determining time are subvertible, resulting in widespread security loss. Worse yet, we do not have security notions for network time protocols that (a) can be rigorously asserted and (b) rigorously guarantee security of applications that require a sense of real time. We propose such notions, within the universally composable (UC) security framework. That is, we formulate ideal functionalities that capture a number of prevalent forms of time measurement within existing systems. We show how they can be realized by realworld protocols, and how they can be used to assert security of timereliant applications  specifically, certificates with revocation and expiration times. This allows for relatively clear and modular treatment of the use of time in securitysensitive systems. Our modeling and analysis are done within the existing UC framework, in spite of its asynchronous, eventdriven nature. This allows incorporating the use of real time within the existing body of analytical work done in this framework. In particular it allows for rigorous incorporation of real time within cryptographic tools and primitives. With Ran Canetti, Kyle Hogan, and Mayank Varia 
Fall Semester, 2017
Dec 06, 2017 12:00PM 
Prashant Vasudevan, MIT 108 WVG Abstract We present functions that are hard to compute on average for algorithms running in some fixed polynomial time, assuming widelyconjectured worstcase hardness of certain problems from the study of finegrained complexity. We discuss the relevance of such averagecase hardness to cryptography and present, as an illustration, an outline of a proofofwork protocol constructed based on the hardness and certain structural properties of our functions. Joint work with Marshall Ball, Alon Rosen and Manuel Sabin. 
Nov 29, 2017 12:00PM 
Ran Cohen, NEU 366 WVH Abstract In the setting of secure multiparty computation (MPC), a set of mutually distrusting parties wish to jointly compute a function, while guaranteeing the privacy of their inputs and the correctness of the output. An MPC protocol is called fully secure if no adversary can prevent the honest parties from obtaining their outputs. A weaker definition is fairness ensuring that an adversary can prematurely abort the computation only before learning any new information. We present highly efficient transformations from fair computations to fully secure computations, assuming the fraction of honest parties is constant (e.g., 1% of the parties are honest). One application of these transformations is a new coinflipping protocol, whose round complexity has a superlogarithmic dependency on the security parameter, improving over the linear dependency on the number of parties in Beimel, Omri, and Orlov (Crypto 2010). A second application is a new fully secure protocol for computing the Boolean OR function, with a superconstant round complexity, improving over the protocol of Gordon and Katz (TCC 2009) whose round complexity is linear in the number of corrupted parties. Finally, we prove that for some functions, a superconstant number of invocations of the fair computation is necessary for computing the function in a fully secure manner. This is a joint work with Eran Omri, Iftach Haitner, and Lior Rotem. 
Nov 15, 2017 12:00PM 
Wolfgang Gatterbauer, NEU 366 WVH Abstract We develop upper and lower bounds for the probability of monotone Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach "dissociation" and give an exact characterization of optimal oblivious bounds, i.e. when the new probabilities are chosen independent of the probabilities of all other variables. Our motivation comes from the weighted model counting problem (or, equivalently, the problem of computing the probability of a Boolean function), which is #Phard in general. By performing several dissociations, one can transform a Boolean formula whose probability is difficult to compute, into one whose probability is easy to compute, and which is guaranteed to provide an upper or lower bound on the probability of the original formula by choosing appropriate probabilities for the dissociated variables. Our bounds shed light on the connection between previous relaxationbased and modelbased approximations and unify them as concrete choices in a larger design space. We also show how our theory allows a standard relational database management system to both upper and lower bound hard probabilistic queries in guaranteed polynomial time. Based on joint work with Dan Suciu from TODS 2014. 
Nov 08, 2017 12:00PM 
Siyao Guo, NEU 366 WVH Abstract We initiate a quantitative study of the power of negations, asking how many negations are required to compute cryptographic primitives. We provide several lower bounds, some of them tight, for various cryptographic primitives and building blocks including oneway permutations, pseudorandom functions, smallbias generators, hardcore predicates, errorcorrecting codes, and randomness extractors. Among our results, we highlight the following.
In addition, we will mention some recent results in understanding the power of negations from multiple angles including Boolean formulas and property testing. Based on join works with Clément L. Canonne, Elena Grigorescu, Ilan Komargodski, Akash Kumar, Tal Malkin, Igor C. Oliveria, Alon Rosen, and Karl Wimmer. 
Nov 01, 2017 12:00PM 
Theory Lunch  no talk 142 ISEC 
Oct 25, 2017 12:00PM 
Mika Göös, Harvard 366 WVH Abstract For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a "lifted" twoparty version of F is hard to refute in any proof system whose lines are computed by efficient communication protocolsor, equivalently, that a monotone function associated with F has large monotone circuit complexity. Our result extends to real monotone circuits, which yields new lower bounds for the Cutting Planes proof system. Joint work with Ankit Garg, Pritish Kamath, and Dmitry Sokolov. 
Oct 18, 2017 12:00PM 
Ali Vakilian, MIT 366 WVH Abstract We study the Fractional Set Cover problem in the streaming model. That is, we consider the relaxation of the set cover problem over a universe of $n$ elements and a collection of $m$ sets, where each set can be picked fractionally, with a value in $[0, 1]$. We present a randomized $(1+ \epsilon)$approximation algorithm that makes $p$ passes over the data, and uses $O(\textit{polylog} (m, n, 1/\epsilon)(mn^{(O(1/(p \epsilon))})+ n))$ memory space. The algorithm works in both the set arrival and the edge arrival models. To the best of our knowledge, this is the first streaming result for the fractional set cover problem. We obtain our results by employing the multiplicative weights update framework in the streaming settings. 
Oct 11, 2017 12:00PM 
Matt Dippel + Tanay Mehta 366 WVH 
Oct 04, 2017 12:00PM 
Yashvanth Kondi 366 WVH Abstract Garbled circuits are of central importance in cryptography, finding widespread application in secure computation, zeroknowledge (ZK) protocols, and verifiable outsourcing of computation to name a few. We are interested in a particular kind of garbling scheme, termed privacyfree in the literature. We show that Boolean formulas can be garbled informationtheoretically in the privacyfree setting, producing no ciphertexts at all. Existing garbling schemes either rely on cryptographic assumptions (and thus require cryptographic operations to construct and evaluate garbled circuits), produce garbled circuits of nonzero size, or are restricted to low depth formulaic circuits. Our result has both theoretical and practical implications for garbled circuits as a primitive. On the theory front, our result breaks the known theoretical lower bound of one ciphertext for garbling an AND gate in this setting. As an interesting implication of producing size zero garbled circuits, our scheme scores adaptive security for free. On the practical side, our garbling scheme involves only cheap XOR operations and produces size zero garbled circuits. As a side result, we propose several interesting extensions of our scheme. Namely, we show how to garble threshold and high fanin gates. An aspect of our garbling scheme that we believe is of theoretical interest is that it does not maintain the invariant that the garbled circuit evaluator must not at any point be in possession of both keys of any wire in the garbled circuit. 
Sep 27, 2017 12:00PM 
Ariel Hamlin 366 WVH Abstract Protected database search systems cryptographically isolate the roles of reading from, writing to, and administering the database. This separation limits unnecessary administrator access and protects data in the case of system breaches. Since protected search was introduced in 2000, the area has grown rapidly; systems are offered by academia, startups, and established companies. However, there is no best protected search system or set of techniques. Design of such systems is a balancing act between security, functionality, performance, and usability. This challenge is made more difficult by ongoing database specialization, as some users will want the functionality of SQL, NoSQL, or NewSQL databases. This database evolution will continue, and the protected search community should be able to quickly provide functionality consistent with newly invented databases. At the same time, the community must accurately and clearly characterize the tradeoffs between different approaches. To address these challenges, we provide the following contributions: 1) An identification of the important primitive operations across database paradigms. We find there are a small number of base operations that can be used and combined to support a large number of database paradigms. 2) An evaluation of the current state of protected search systems in implementing these base operations. This evaluation describes the main approaches and tradeoffs for each base operation. Furthermore, it puts protected search in the context of unprotected search, identifying key gaps in functionality. 3) An analysis of attacks against protected search for different base queries. 4) A roadmap and tools for transforming a protected search system into a protected database, including an opensource performance evaluation platform and initial user opinions of protected search. 
Spring Semester, 2017
Apr 27, 2017 3:30PM 
Omri Weinstein, Columbia 366 WVH Abstract We prove the first superlogarithmic lower bounds on the cell probe complexity of dynamic *boolean* (a.k.a. decision) data structure problems, a longstanding milestone in data structure lower bounds. We introduce a new technique and use it to prove a ~ $\log^{1.5}(n)$ lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting *over $GF_2$* ([Pat07]). Proving an $\omega(\log n)$ lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai Patrascu's obituary [Tho13]. This result also implies the first $\omega(\log n)$ lower bound for the classical 2D range counting problem, one of the most fundamental data structure problems in computational geometry and spatial databases. We derive similar lower bounds for boolean versions of dynamic polynomial evaluation and 2D "rectangle stabbing", and for the (nonboolean) problems of range selection and range median. Our technical centerpiece is a new way of "weakly" simulating dynamic data structures using efficient *oneway* communication protocols with small advantage over random guessing. This simulation involves a surprising excursion to lowdegree (Chebychev) polynomials which may be of independent interest, and offers an entirely new algorithmic angle on the "cell sampling" method of Panigrahy et al. [PTW10]. Joint work with Kasper GreenLarsen and Huacheng Yu. 
Apr 20, 2017 3:30PM 
Ankur Moitra, MIT RY 126 Abstract Starting from the seminal works of Tukey (1960) and Huber (1964), the field of robust statistics asks: Are there estimators that provably work in the presence of noise? The trouble is that all known provably robust estimators are also hard to compute in highdimensions. Here, we study a basic problem in robust statistics, posed in various forms in the above works. Given corrupted samples from a highdimensional Gaussian, are there efficient algorithms to accurately estimate its parameters? We give the first algorithms that are able to tolerate a constant fraction of corruptions that is independent of the dimension. Additionally, we give several more applications of our techniques to product distributions and various mixture models. This is based on joint work with Ilias Diakonikolas, Jerry Li, Gautam Kamath, Daniel Kane and Alistair Stewart. 
Apr 13, 2017 3:30PM 
No seminar 
Apr 06, 2017 3:30PM 
No seminar 
Mar 30, 2017 3:30PM 
Ariel Hamlin and Lucianna Kiffer 366 WVH 
Mar 23, 2017 3:30PM 
Mehraneh Liaee, NEU 366 WVH Abstract We study the problem of gossip in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, $n$ tokens are arbitrarily distributed among the $n$ network nodes, and the goal is to disseminate all the n tokens to every node. Our focus is on tokenforwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. Gossip can be completed in linear time in any static network, but a basic open question for dynamic networks is the existence of a distributed protocol that can do significantly better than an easily achievable bound of $O(n^2)$ rounds. In previous work, it has been shown that under adaptive adversaries, every token forwarding algorithm requires $\Omega(n^2/\log n)$ rounds. In this paper, we study oblivious adversaries, which differ from adaptive adversaries in one crucial aspect they are oblivious to random choices made by the protocol. We present an $\tilde{\Omega}(n^{3/2})$ lower bound under an oblivious adversary for RANDDIFF, a natural algorithm in which neighbors exchange a token chosen uniformly at random from the difference of their token sets. We also present an $\tilde{\Omega}(n^{4/3})$ bound under a stronger notion of oblivious adversary for symmetric knowledgebased algorithms. On the positive side, we present a centralized algorithm that completes gossip in $\tilde{\Omega}(n^{3/2})$ rounds. We also show an $\tilde{O}(n^{5/3})$ upper bound for RANDDIFF in a restricted class of oblivious adversaries, which we call pathsrespecting. 
Mar 16, 2017 3:30PM 
Yael Kalai, MIT/MSR 366 WVH Abstract We construct an interactive coding scheme, a notion introduced by Schulman (FOCS 1992, STOC 1993). Loosely speaking, we show how to convert any twoparty interactive protocol into one that is resilient to constantfraction of *insertion* and *deletion* errors, while preserving computational efficiency, and blowing up the communication complexity and the *round* complexity by a constant factor that approaches 0 as the errorrate approaches 0. Previous works were not concerned with the round complexity, and typically assumed that one bit is sent per round. Moreover, most previous works (with the exception of the recent work of Braverman et. al.) considered only substitution errors or erasures errors. We consider the model where in each round each party may send a message of *arbitrary*, where the length of the messages and the length of the protocol may be adaptive, and may depend on the private inputs of the parties and on previous communication. This model is known as the (synchronous) message passing model, and is commonly used in distributed computing, and is the most common model used in cryptography. This is joint work with Klim Efremenko and Elad Haramaty. 
Mar 9, 2017 3:30PM 
No seminar  Spring Break 
Mar 2, 2017 3:30PM 
Gautam Kamath, MIT 366 WVH Abstract Given samples from an unknown distribution p, does it have some property, or is it far from every distribution possessing this property? This question has received enormous attention in statistics, information theory, and theoretical computer science. Some properties of interest include:
In this talk, I will discuss some recent results and directions on the frontiers of distribution testing. The main focus will be on testing whether a distribution belongs to a particular class, but I'll also talk about some newer directions, including testing on highdimensional domains under structural assumptions (i.e., where the underlying distribution is a graphical model) and testing while maintaining differential privacy. Based on joint works with Jayadev Acharya, Bryan Cai, Constantinos Daskalakis, and Nishanth Dikkala. 
Feb 21, 2017 3:30PM 
Jalaj Upadhyay, Penn State 366 WVH Abstract The problem of lowrank factorization of an m x n matrix $A$ requires outputting a singular value decomposition: an m x k matrix $U$, an n x k matrix $V$, and a k x k diagonal matrix $D$ such that $U D V^T$ approximates the matrix $A$ in the Frobenius norm. In this talk, we study releasing differentiallyprivate lowrank factorization of a matrix in the general turnstile update model. We give a differentiallyprivate algorithm instantiated with respect to a privacy level stronger than privacy levels for this and related problems studied in previous works, namely that of Blocki et al.(FOCS 2012), Dwork et al. (STOC 2014), Hardt and Roth (STOC 2012, STOC 2013), and Hardt and Price (NIPS 2014). We consider two matrices $A$ and $A'$ as neighboring if $A  A'$ can be represented as an outer product of two unit vectors. Our private algorithm with respect to this privacy level incurs optimal additive error. We also prove a lower bound that shows that the space required by this algorithm is optimal up to a logarithmic factor. Based on the paper arXiv:1604.01429 
Feb 16, 2017 3:30PM 
Adam Sealfon, MIT 366 WVH Abstract Motivated by the goal of improving the concrete efficiency of secure multiparty computation (MPC), we study the possibility of implementing an infrastructure for MPC. We propose an infrastructure based on oblivious transfer (OT), which would consist of OT channels between some pairs of parties in the network. We devise informationtheoretically secure protocols that allow additional pairs of parties to establish secure OT correlations using the help of other parties in the network in the presence of a dishonest majority. Our main technical contribution is an upper bound that matches a lower bound of Harnik, Ishai, and Kushilevitz (Crypto 2007), who studied the number of OT channels necessary and sufficient for MPC. In particular, we characterize which nparty OT graphs G allow tsecure computation of OT correlations between all pairs of parties, showing that this is possible if and only if the complement of G does not contain as a subgraph the complete bipartite graph $K_{nt,nt}$. Joint work with Ranjit Kumaresan and Srinivasan Raghuraman. 
Feb 9, 2017 3:30PM 
Talk cancelled due to weather 
Feb 2, 2017 3:30PM 
Constantinos Daskalakis, MIT 108 WVH Abstract We provide global convergence guarantees for the expectationmaximization (EM) algorithm applied to mixtures of two Gaussians with known covariance matrices. We show that EM converges geometrically to the correct mean vectors, and provide simple, closedform expressions for the convergence rate. As a simple illustration, we show that in one dimension ten steps of the EM algorithm initialized at infinity result in less than 1% error estimation of the means. Joint work with Christos Tzamos and Manolis Zampetakis. 
Jan 26, 2017 3:30PM 
No talk 
Jan 19, 2017 3:30PM 
Stratis Ioannidis, Northeastern 366 WVH Abstract Secure Function Evaluation (SFE) allows an interested party to evaluate a function over private data without learning anything about the inputs other than the outcome of this computation. This offers a strong privacy guarantee: SFE enables, e.g., a medical researcher, a statistician, or a data analyst, to conduct a study over private, sensitive data, without jeopardizing the privacy of the study's participants (patients, online users, etc.). Nevertheless, applying SFE to "big data" poses several challenges. First, beyond any computational overheads due to encryptions and decryptions, executing an algorithm securely may lead to a polynomial blowup in the total work compared to execution in the clear. For large datasets, even going from linear to quadratic complexity is prohibitive. Second, secure evaluations of algorithms should also maintain parallelizability: an algorithm that is easy to parallelize in the clear should also maintain this property in its SFE version, if its execution is to scale. This poses a challenge, as communication patterns between processors may reveal a lot about the private inputs. In this talk, we show that several machine learning and data mining algorithms can be executed securely while leading to only (a) a logarithmic blowup in total work and (b) a logarithmic increase in the execution time when executed in parallel. Our techniques generalize to any algorithm that is graphparallel, i.e., can be expressed through a sequence of scatter, gather, and apply operations. This includes several algorithms of practical interest, including page rank, matrix factorization, and training neural networks. 
Jan 12, 2017 3:30PM 
Jonathan Ullman, Northeastern 366 WVH Abstract Adaptivity is an important feature of data analysis  the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model, where all questions are specified before the dataset is drawn. Recent work by Dwork et al. (STOC, 2015) and Hardt and Ullman (FOCS, 2014) initiated a general formal study of this problem, and gave the first upper and lower bounds on the achievable generalization error for adaptive data analysis. Specifically, suppose there is an unknown distribution $P$ and a set of $n$ independent samples $x$ is drawn from $P$. We seek an algorithm that, given $x$ as input, accurately answers a sequence of adaptively chosen "queries" about the unknown distribution $P$. How many samples $n$ must we draw from the distribution, as a function of the type of queries, the number of queries, and the desired level of accuracy? We give new upper bounds on the number of samples n that are needed to answer statistical queries. The bounds improve and simplify the work of Dwork et al. (STOC, 2015), and have been applied in subsequent work by those authors (Science, 2015; NIPS, 2015). As in Dwork et al., our algorithms are based on a connection with algorithmic stability in the form of differential privacy. We extend their work by giving a quantitatively optimal, more general, and simpler proof of their main theorem that the stability notion guaranteed by differential privacy implies low generalization error. Joint work with Raef Bassily, Kobbi Nissim, Adam Smith, Thomas Steinke, and Uri Stemmer. 
Jan 03, 2017 2:00PM 
LiYang Tan, TTIChicago 166 WVH Abstract
We consider the fundamental derandomization problem of deterministically finding a satisfying assignment to a CNF formula that has many satisfying assignments. We give a deterministic algorithm which, given an $n$variable $poly(n)$clause CNF formula $F$ that has $F1(1) /eq \epsilon 2n$, runs in time $nO^~(loglogn)2$ for $\epsilon \geq 1/\polylog(n)$ and outputs a satisfying assignment of $F$. Prior to our work the fastest known algorithm for this problem was simply to enumerate over all seeds of a pseudorandom generator for CNFs; using the best known PRGs for CNFs [DETT10], this takes time $n\Omega^~(logn)$ even for constant $\epsilon$. Joint work with Rocco Servedio.

Fall Semester, 2016
Sep 21, 2016 12:30PM 
Daniel Wichs and Jack Doerner 366 WVH 
Sep 28, 2016 12:30PM 
Yaron Singer, Harvard 366 WVH Abstract
In this talk we will consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, with many algorithms that provide desirable approximation guarantees. However, in many applications we do not have access to the function we aim to optimize, but rather to some erroneous or noisy version of it. This raises the question of whether provable guarantees are obtainable in presence of error and noise. We provide initial answers, by focusing on the question of maximizing a monotone submodular function under a cardinality constraint when given access to a noisy oracle of the function.

Oct 05, 2016 12:15PM 
Huy Nguyen, Northeastern 366 WVH Abstract In the turnstile L_p heavy hitters problem with parameter eps, one must maintain a highdimensional vector x in R^n subject to updates of the form update(i, Delta), which increases x_i by Delta, where i is in [n], and Delta is an integer. Upon receiving a query, the goal is to report every ``heavy hitter'' i in[n] with x_i >= eps*x_p as part of a list L, which is a subset of [n] of size O(1/\eps^p), i.e. proportional to the maximum possible number of heavy hitters. In fact we solve the stronger tail version, in which L should include every i such that x_i >= \eps x_{proj{1/eps^p}}_p and x_i > 0, where x_{proj{k}} denotes the vector obtained by zeroing out the largest k entries of x in magnitude. We provide a new algorithm, which in the most general turnstile model achieves optimal O(\eps^{p}\log n) space, O(\log n) update time, and fast O(\eps^{p}\poly(\log n)) query time, providing correctness whp. Our main innovation is an efficient reduction from the heavy hitters to a clustering problem in which each heavy hitter is encoded as some form of noisy spectral cluster in a much bigger graph, and the goal is to identify every cluster. Since every heavy hitter must be found, correctness requires that every cluster be found. We thus need a ``clusterpreserving clustering'' algorithm, that partitions the graph into clusters with the promise of not destroying any original cluster. To do this we first apply standard spectral graph partitioning, and then we use some novel combinatorial techniques to modify the cuts obtained so as to make sure that the original clusters are sufficiently preserved. Our clusterpreserving clustering may be of broader interest much beyond heavy hitters. Joint work with Kasper Green Larsen, Jelani Nelson, and Mikkel Thorup. 
Oct 12, 2016 12:30PM 
Mohsen Ghaffari, MIT/ETH Zurich 366 WVH (Abstract) How can the computers in a network interact and communicate to solve the network's graph problems efficiently? This is the subject of the area of (local) distributed graph algorithms, which dates back to the 1980s. The recent years have witnessed significant developments in this classical area. In this talk, we survey some of these developments. Noting the gap between randomized and deterministic distributed graph algorithms, the talk has three (closelyrelated) parts: 1) On the randomized side, we present the first nearlyoptimal randomized distributed algorithm for maximal independent set. Using wellknown reductions, this provides a unified efficient algorithm for all the classical problems of the area. 2) On the deterministic side, we present an improved deterministic distributed algorithm for edge coloring, which almost settles a quartercentury old open problem. 3) We conclude with mentioning a surprising result that pinpoints the gap between randomized and deterministic distributed algorithms: we present a rudimentarylooking rounding problem, which admits a trivial 0round randomized algorithm, and prove that if one can solve it deterministically in polylog(n) rounds, we would get polylog(n)round deterministic distributed algorithms for all the local problems. The latter remains the most wellknown open question of the area. 
Oct 19, 2016 12:30PM 
Mor Weiss, Northeastern 366 WVH (Abstract) In the past few decades, probabilistic checking techniques were shown to yield dramatic efficiency improvements in verifying proofs and approximating distance from errorcorrecting codes. We show connections between cryptography and "zeroknowledge" variants of these techniques, such as Probabilistically Checkable Proofs (PCPs) and PCPs of Proximity (PCPPs), and use them to improve the complexity of cryptographic protocols. In this talk we will discuss two constructions: 1. PCPs for NP with zeroknowledge guarantees, that can be verified nonadaptively, namely by making a single round of queries to the proof. Our construction is based on a novel connection to leakageresilient circuits. 2. Zeroknowledge PCPPs for NP, a generalization of zeroknowledge PCPs, which we construct by combining standard PCPPs with secure multiparty computation protocols. Based on joint works with Yuval Ishai, Amit Sahai, Michael Viderman and Guang Yang. 
Oct 26, 2016 12:30PM 
Matt Dippel and Chin Ho Lee 366 WVH 
November 1, 2016 12:30PM 
Lorenzo Orecchia, Boston University 366 WVH (Abstract) Fast iterative methods from Convex Optimization play a crucial role in a number of recent breakthroughs in the design of nearlylineartime algorithms for fundamental combinatorial problems, such as maximum flow and graph partitioning. Multiplicative Weight Updates, Gradient Descent, and Nesterov's Method have become a mainstay in the construction and analysis of fast algorithms. The power of these approaches raises a number of questions: What is the exact relation between Multiplicative Weight Updates and Gradient Descent? Why do Multiplicative Weight Updates show up in so many settings? What is the intuition behind Nesterov's iterative algorithm that achieves the asymptotically optimal iteration count for smooth convex functions? In this survey talk, I will provide answers by presenting a unified framework that reveals the power and limitations of each method and provides much needed geometric intuition. Among other insights, I will explain how Multiplicative Weight Updates are a particular instance of a dual iterative method, known as Mirror Descent, and how Nesterov's algorithm can be naturally derived as a combination of Mirror and Gradient Descent. As an example of the application of these insights, I will also discuss their crucial role in recent progress in the nearlylineartime solution of packing linear programs, both in parallel and sequentially. 
Nov 9, 2016 12:30PM 
Mitali Bafna and Hamid Jahanjou 366 WVH 
Nov 16, 2016 12:30PM 
Harry Lang, Johns Hopkins 366 WVH (Abstract) In the streaming model, data points arrive sequentially and algorithms attempt to use a sublinear amount of memory. For a class of clustering functions (including kmeans, kmedian, and L_p norms), we introduce a new technique for converting a coreset construction in the RAM model into a coreset construction in the streaming model. On a stream of n points, our method yields streaming coreset algorithms requiring the storage of O(S + k log n) points, where S is the size of the coreset. The previous stateoftheart required O(S log^3 n) points. Note that S = \Omega(k), so this improves all parameters. In the RAM setting, we improve the size of coresets for a larger class of problems. This includes coresets for kmeans with nonnegative weights that depend on k as k \log k, and a Euclidean construction where the coreset size is independent of the dimension. 
Nov 23, 2016 
Thanksgiving  No Seminar 
Nov 30, 2016 12:30PM 
Ankit Garg, MSR 411 Ell Hall (Abstract) The celebrated BrascampLieb (BL) inequalities (and their extensions) are
an important mathematical tool, unifying and generalizing numerous inequalities in analysis,
convex geometry and information theory. While their structural theory is very well understood,
far less is known about computing their main parameters. We give polynomial time algorithms to compute: The algorithms are obtained by a simple efficient reduction of a given BLdatum to an instance of the Operator Scaling problem defined by Gurvits, for which the present authors provided a polynomial time algorithm recently. This will be based on joint work with Leonid Gurvits, Rafael Oliveira and Avi Wigderson. 
Dec 07, 2016 12:30PM 
Vitaly Shmatikov, Cornell Tech 411 Ell Hall (Abstract) Mylar is a framework by Popa et al. that uses multikey searchable encryption (MKSE) to build Web applications on top of encrypted data. We demonstrate that (1) the PopaZeldovich model for MKSE does not imply security against either passive or active attacks; (2) Mylarbased Web applications reveal users’ data and queries to passive and active adversarial servers; and (3) Mylar is generically insecure against active attacks due to system design flaws. Our results show that the problem of securing clientserver applications against actively malicious servers is challenging and still unsolved. 
Spring Semester, 2016
Jun 16, 2016 3:30PM 
Ryan Rogers, University of Pennsylania 366 WVH (Abstract)
In this work, we initiate a principled study of how the generalization properties of approximate differential privacy can be used to perform adaptive hypothesis testing, while giving statistically valid pvalue corrections. We do this by observing that the guarantees of algorithms with bounded approximate maxinformation are sufficient to correct the pvalues of adaptively chosen hypotheses, and then by proving that algorithms that satisfy (approximate) (epsilon,delta)differential privacy have bounded approximate max information when their inputs are drawn from a product distribution. This substantially extends the known connection between differential privacy and maxinformation, which previously was only known to hold for (pure) (epsilon,0)differential privacy. It also extends our understanding of maxinformation as a partially unifying measure controlling the generalization properties of adaptive data analyses. We also show a lower bound, proving that (despite the strong composition properties of maxinformation), when data is drawn from a product distribution, approximate differentially private algorithms can come first in a composition with other algorithms satisfying maxinformation bounds, but not necessarily second if the composition is required to itself satisfy a nontrivial maxinformation bound. This, in particular, implies that the connection between approximate differential privacy and maxinformation holds only for inputs drawn from product distributions, unlike the connection between pure differential privacy and maxinformation.

Apr 14, 2016 2:50PM 
Gabor Lippner, Northeastern University Dept. of Mathematics 366 WVH (Abstract)
A local algorithm aims to compute some global structure on a graph using only simultaneous, local, decisions at the nodes. I will review recent developments on the possibilities and the limitations of such algorithms, and explain their connection to the theory of graph limits.

Apr 7, 2016 1:30PM 
Huy Nguyen, TTI Chicago 366 WVH (Abstract)
Challenges abound in modern large scale data analysis, ranging from the sheer volume of the data to its complex structure and the need for timely responses. A promising common approach centers on capturing key information from the data using concise representations that can be constructed in a distributed manner or from an evolving stream of data. In this talk, we will illustrate both the power and limitations of this approach using three research vignettes. In the first example, we describe an algorithmic framework for fundamental linear algebra problems based on short summaries. In the second example, we design distributed algorithms for a family of nonconvex problems arising in learning applications. In the third example, we show that even basic statistical estimation tasks require large summaries.

Apr 4, 2016 10:30AM 
Matt Weinberg, Princeton 366 WVH (Abstract) When real people interact with algorithms (e.g. in auctions, crowdsourcing, Bitcoin, etc.), they impose additional desiderata beyond simply that the algorithm is correct, fast, and uses little storage. People strategize during these interactions, so algorithms deployed in these settings must be robust against strategic manipulation. Additionally, people prefer transparent interactions, so these algorithms must also be as simple as possible. My research addresses these, and other novel challenges that arise when algorithms interact with strategic agents. In this talk, I will focus on robustness against strategic manipulation, and present a new algorithmic framework for these settings. Specifically, I will present a blackbox reduction from solving any optimization problem in strategic settings, where the input is held by selfish agents with interests of their own, to solving a perturbed version of that same optimization problem in traditional settings, where the input is directly given. I will further apply this framework to resolve two longstanding open problems: extending Myerson's celebrated characterization of optimal singleitem auctions to multiple items (Myerson 1981), and designing truthful mechanisms for job scheduling on unrelated machines (Nisan and Ronen 1999). Finally, I will briefly show how strategic considerations motivate nice questions in "traditional" areas of algorithm design as well, and present some of my work in convex optimization, parallel algorithms, and prophet inequalities. 
Mar 23, 2016 10:30AM 
Sofya Raskhodnikova, Penn State 366 WVH (Abstract) Massive datasets are becoming increasingly common. What useful computations can be performed on a dataset when reading all of it is prohibitively expensive? This question, fundamental to several fields, is at the heart of the research area, called sublineartime algorithms, that has provided important insights into fast approximate computation. In this talk, we will consider types of computational tasks central to sublineartime algorithms: approximation, testing, and learning. We will see examples of sublineartime algorithms in several domains. The algorithms themselves are typically simple and efficient, but their analysis requires insights into basic combinatorial, algebraic, and geometric questions. We will also discuss new directions in sublineartime algorithms, including new computational tasks, new measures for accuracy guarantees, and new models for data access. These directions enable applications of sublineartime algorithms in privacy, analysis of realvalued data, and situations where the data is noisy or incomplete. 
Mar 16, 2016 10:30AM 
Mohit Singh, Microsoft Research Redmond 366 WVH (Abstract) In this talk I will discuss the problem of computing maximum entropy distributions over a discrete set of objects subject to observed marginals. While there has been a tremendous amount of interest in such distributions due to their applicability in areas such as statistical physics, economics, information theory, machine learning, combinatorics and algorithms, a rigorous and systematic study of how to compute such distributions had been lacking. In this talk, I will show that the problem of computing maximum entropy distributions, in a fairly general setting, is equivalent to a counting problem on the underlying set. One of the consequences of this equivalence is that, for several combinatorial settings, there is an efficient algorithm to compute maxentropy distributions. I will also talk about applications of maximum entropy distributions to design approximation algorithms for discrete optimization problems including the Traveling Salesman Problem (TSP). These results include the first improvements over the classical Christofides' algorithm from 1970's for TSP on graph metrics. 
Mar 15, 2016 4:00PM 
Nils Olberg, Aachen 366 WVH (Abstract) In the concurrent multicast problem, we are given a graph representing a communication network together with a set of senderreceiver pairs. The goal is to deliver the message of each sender to the corresponding receiver. The concurrent multicast problem and its variants are motivated by information dissemination problems arising in diverse network scenarios. In this talk, we consider two of the most prominent communication models, namely the telephone and the radio model. For each of these models, our aim to develop algorithms that give good approximation algorithms, since the underlying problems are known to be NPhard. Using sparse partition covers we provide a first nontrivial bound for radio concurrent multicast. We further demonstrate the connection of telephone concurrent multicast to other network design problems, which motivates the development of approximation algorithms for the latter. Finally, we show that our methods can be extended to yield new results for minimum degree graph spanners. 
Mar 14, 2016 10:30AM 
Vipul Goyal, Microsoft Research India 366 WVH (Abstract) A central challenge in the design of secure systems is to defend against maninthemiddle attacks, where an adversary can arbitrarily tamper with the messages exchanged by two parties over a communication channel. Starting with the early nineties, an important research goal in cryptography has been to build ``nonmalleable'' cryptographic protocols that are resilient to such attacks. In this talk, I will describe my work that culminates this twodecade long research quest by constructing roundoptimal nonmalleable protocols based on almost minimal cryptographic assumptions. I will also discuss how the techniques developed in these works have transcended cryptography and found applications in randomness extraction, coding theory, and complexity theory. I will also briefly talk about my work on applied cryptography and its impact. 
Feb 29, 2016 10:30AM 
Timothy Chan, University of Waterloo 366 WVH (Abstract) Although data structures in computational geometry have been studied since the 1970s, recent years have seen exciting new developments that deepen our theoretical understanding of some of the most fundamental problems in the area. In this talk, I will survey work on a number of these core problems, including (static and dynamic) 2D point location, 2D nearest neighbor searching, and orthogonal and nonorthogonal range searching. If time permits, I will also mention some unexpected applications of geometric data structures, to text indexing and allpairs shortest paths. 
Feb 9, 2016 10:30AM 
Mary Wootters, Carnegie Mellon University 366 WVH (Abstract) Error correcting codes are an important tool in communication, and the family of ReedSolomon (RS) codes is an especially important example. I'll introduce error correcting and ReedSolomon codes, and I'll talk about three very different ways that RS codes have come up in my research. These three ways (none of which immediately has to do with communication) run the gamut from theory to practice. The first way, on the very theoretical end, is a combinatorial problem called list decoding, which has motivations in complexity theory. The second way, a bit more downtoearth, has to do with designing schemes for distributed storage: how do we store a file on several servers robustly? The third way, on the practical side of things, is combinatorial group testing: in our work we collaborated with computational biologists to design better algorithms for highthroughput genetic screening and de novo gene sequencing. 
Jan 21, 2016 3:30PM 
Zhiwei Steven Wu, University of Pennsylvania 366 WVH (Abstract) We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among n parties, who need to each choose an action, which jointly will form a solution to the optimization problem. The coordination complexity represents the minimal amount of information that a centralized coordinator, who has full knowledge of the problem instance, needs to broadcast in order to coordinate the n parties to play a nearly optimal solution. We show that upper bounds on the coordination complexity of a problem imply the existence of good jointly differentially private algorithms for solving that problem, which in turn are known to upper bound the price of anarchy in certain games with dynamically changing populations. We show several results. We fully characterize the coordination complexity for the problem of computing a manytoone matching in a bipartite graph by giving almost matching lower and upper bounds.Our upper bound in fact extends much more generally, to the problem of solving a linearly separable convex program. We also give a different upper bound technique, which we use to bound the coordination complexity of coordinating a Nash equilibrium in a routing game, and of computing a stable matching. 
Jan 6, 2016 12:00PM 
ChienChung Huang, Chalmers University of Technology 366 WVH (Abstract) We propose new exact and approximation algorithms for the weighted matroid intersection problem. Our exact algorithm is faster than previous algorithms when the largest weight is relatively small. Our approximation algorithm delivers a $(1\epsilon)$approximate solution with a running time significantly faster than most known exact algorithms. The core of our algorithms is a decomposition technique: we decompose an instance of the weighted matroid intersection problem into a set of instances of the unweighted matroid intersection problem. The computational advantage of this approach is that we can make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms. Precisely speaking, we prove that we can solve the weighted matroid intersection problem via solving $W$ instances of the unweighted matroid intersection problem, where $W$ is the largest given weight. Furthermore, we can find a $(1\epsilon)$approximate solution via solving $O(\epsilon^{1} \log r)$ instances of the unweighted matroid intersection problem, where $r$ is the smallest rank of the given two matroids. 
Fall Semester, 2015
Dec 8, 2015 3:30PM 
Elliot Anshelevich, RPI 366 WVH (Abstract)
We examine the quality of social choice mechanisms using a utilitarian view, in which all of the agents have costs for each of the possible alternatives. While these underlying costs determine what the optimal alternative is, they may be unknown to the social choice mechanism; instead the mechanism must decide on a good alternative based only on the ordinal preferences of the agents which are induced by the underlying costs. Due to its limited information, such a social choice mechanism cannot simply select the alternative that minimizes the total social cost (or minimizes some other objective function). Thus, we seek to bound the distortion: the worstcase ratio between the social cost of the alternative selected and the optimal alternative. Distortion measures how good a mechanism is at approximating the alternative with minimum social cost, while using only ordinal preference information. The underlying costs can be arbitrary, implicit, and unknown; our only assumption is that the agent costs form a metric space, which is a natural assumption in many settings. We quantify the distortion of many wellknown social choice mechanisms. We show that for both total social cost and median agent cost, many positional scoring rules have large distortion, while on the other hand Copeland and similar mechanisms perform optimally or nearoptimally, always obtaining a distortion of at most 5. We also give lower bounds on the distortion that could be obtained by *any* deterministic social choice mechanism, and extend our results on median agent cost to more general objective functions.

Nov 12, 2015 3:30PM 
Cris Moore, Santa Fe Institute 177 Huntington Ave, 11th Floor (Abstract) October 22, 3:305:00 PM Lecture I: Computational complexity and landscapes o Two puzzles: Euler vs. Hamilton o P vs. NP and NPcompleteness: building computers o When greed works: Minimum Spanning Tree and Max Flow o Bumpy energy landscapes and local optima October 29, 3:305:00 PM Lecture II: Phase transitions in random graphs o The emergence and size of the giant component o Branching processes and differential equations o Power laws at criticality o The kcore and discontinuous transitions November 5, 3:305:00 PM Lecture III: Phase transitions in random kSAT o Early history and phenomenology o First and second moment bounds o Algorithms, clustering, and frozen variables o Why we believe in a regime where solutions exist but are hard to find November 12, 3:305:00 PM Lecture IV: Community detection in networks o The stochastic block model o The analogy between statistical physics and statistical inference o Belief propagation and variational methods o The detectability transition o (If there's time) Spectral clustering 
Nov 10, 2015 12:00PM 
Bobby Kleinberg 366 WVH (Abstract) How much information can be learnt about an individual by observing the outcome of a computation? If the computation is differentially private, the answer is: "not much more than if the individual's data had been excluded from the input." A stronger notion of privacy, originally propounded by Dalenius in the 1970's, requires instead that it should not be possible to learn much more about an individual than if the outcome of the computation had never been revealed. Simple examples, as well as a general impossibility theorem of Dwork and Naor, preclude the possibility of supplying this stronger "inferential" guarantee against attackers with arbitrary auxiliary information, assuming the computation is at least minimally useful. In this talk we revisit the notion of inferential privacy and ask: under what limitations on the adversary's side information can we deduce an inferential guarantee from a differential one? We model the adversary's side information as a prior distribution over datasets (or, more generally, a set of possible priors) and prove two main results. The first result pertains to distributions that satisfy a natural positiveaffiliation condition, and gives an upper bound on the inferential privacy guarantee for any differentially private mechanism. This upper bound is matched by a simple mechanism that adds Laplace noise to the sum of the data. The second result pertains to distributions that have weak correlations, defined in terms of a suitable "influence matrix". The result provides an upper bound for inferential privacy in terms of the differential privacy parameter and the spectral norm of this matrix. 
Nov 5, 2015 3:30PM 
Cris Moore, Santa Fe Institute 177 Huntington Ave, 11th Floor (Abstract) October 22, 3:305:00 PM Lecture I: Computational complexity and landscapes o Two puzzles: Euler vs. Hamilton o P vs. NP and NPcompleteness: building computers o When greed works: Minimum Spanning Tree and Max Flow o Bumpy energy landscapes and local optima October 29, 3:305:00 PM Lecture II: Phase transitions in random graphs o The emergence and size of the giant component o Branching processes and differential equations o Power laws at criticality o The kcore and discontinuous transitions November 5, 3:305:00 PM Lecture III: Phase transitions in random kSAT o Early history and phenomenology o First and second moment bounds o Algorithms, clustering, and frozen variables o Why we believe in a regime where solutions exist but are hard to find November 12, 3:305:00 PM Lecture IV: Community detection in networks o The stochastic block model o The analogy between statistical physics and statistical inference o Belief propagation and variational methods o The detectability transition o (If there's time) Spectral clustering 
Oct 29, 2015 3:30PM 
Cris Moore, Santa Fe Institute 177 Huntington Ave, 11th Floor (Abstract) October 22, 3:305:00 PM Lecture I: Computational complexity and landscapes o Two puzzles: Euler vs. Hamilton o P vs. NP and NPcompleteness: building computers o When greed works: Minimum Spanning Tree and Max Flow o Bumpy energy landscapes and local optima October 29, 3:305:00 PM Lecture II: Phase transitions in random graphs o The emergence and size of the giant component o Branching processes and differential equations o Power laws at criticality o The kcore and discontinuous transitions November 5, 3:305:00 PM Lecture III: Phase transitions in random kSAT o Early history and phenomenology o First and second moment bounds o Algorithms, clustering, and frozen variables o Why we believe in a regime where solutions exist but are hard to find November 12, 3:305:00 PM Lecture IV: Community detection in networks o The stochastic block model o The analogy between statistical physics and statistical inference o Belief propagation and variational methods o The detectability transition o (If there's time) Spectral clustering 
Oct 22, 2015 3:30PM 
Cris Moore, Santa Fe Institute 177 Huntington Ave, 11th Floor (Abstract) October 22, 3:305:00 PM Lecture I: Computational complexity and landscapes o Two puzzles: Euler vs. Hamilton o P vs. NP and NPcompleteness: building computers o When greed works: Minimum Spanning Tree and Max Flow o Bumpy energy landscapes and local optima October 29, 3:305:00 PM Lecture II: Phase transitions in random graphs o The emergence and size of the giant component o Branching processes and differential equations o Power laws at criticality o The kcore and discontinuous transitions November 5, 3:305:00 PM Lecture III: Phase transitions in random kSAT o Early history and phenomenology o First and second moment bounds o Algorithms, clustering, and frozen variables o Why we believe in a regime where solutions exist but are hard to find November 12, 3:305:00 PM Lecture IV: Community detection in networks o The stochastic block model o The analogy between statistical physics and statistical inference o Belief propagation and variational methods o The detectability transition o (If there's time) Spectral clustering 